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Journal of Fluid Mechanics
Journal Prestige (SJR): 1.591
Citation Impact (citeScore): 3
Number of Followers: 159  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0022-1120 - ISSN (Online) 1469-7645
Published by Cambridge University Press Homepage  [373 journals]
  • Upstream vortex and elastic wave in the viscoelastic flow around a
           confined cylinder
    • Authors: Boyang Qin; Paul F. Salipante, Steven D. Hudson, Paulo E. Arratia
      Abstract: Viscoelastic flow past a cylinder is a classic benchmark problem that is not completely understood. Using novel three-dimensional (3D) holographic particle velocimetry, we report three main discoveries of the elastic instability upstream of a single cylinder in viscoelastic channel flow. First, we observe that upstream vortices initiate at the corner between the cylinder and the wall, and grow with increasing flow rate. Second, beyond a critical Weissenberg number, the flow upstream becomes unsteady and switches between two bistable configurations, leading to symmetry breaking in the cylinder axis direction that is highly 3D in nature. Lastly, we find that the disturbance of the elastic instability propagates relatively far upstream via an elastic wave, and is weakly correlated with that in the cylinder wake. The wave speed and the extent of the instability increase with Weissenberg number, indicating an absolute instability in viscoelastic fluids.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.73
      Issue No: Vol. 864 (2019)
  • Statistical state dynamics analysis of buoyancy layer formation via the
           Phillips mechanism in two-dimensional stratified turbulence
    • Authors: Joseph G. Fitzgerald; Brian F. Farrell
      Abstract: Horizontal density layers are commonly observed in stratified turbulence. Recent work (e.g. Taylor & Zhou, J. Fluid Mech., vol. 823, 2017, R5) has reinvigorated interest in the Phillips instability (PI), by which density layers form via negative diffusion if the turbulent buoyancy flux weakens as stratification increases. Theoretical understanding of PI is incomplete, in part because it remains unclear whether and by what mechanism the flux-gradient relationship for a given example of turbulence has the required negative-diffusion property. Furthermore, the difficulty of analysing the flux-gradient relation in evolving turbulence obscures the operating mechanism when layering is observed. These considerations motivate the search for an example of PI that can be analysed clearly. Here PI is shown to occur in two-dimensional Boussinesq sheared stratified turbulence maintained by stochastic excitation. PI is analysed using the second-order S3T closure of statistical state dynamics, in which the dynamics is written directly for statistical variables of the turbulence. The predictions of S3T are verified using nonlinear simulations. This analysis provides theoretical underpinning of PI based on the fundamental equations of motion that complements previous analyses based on phenomenological models of turbulence.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.72
      Issue No: Vol. 864 (2019)
  • Subcritical turbulent condensate in rapidly rotating
           Rayleigh–Bénard convection
    • Authors: Benjamin Favier; Céline Guervilly, Edgar Knobloch
      Abstract: The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows such as atmospheric or oceanic circulations.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.58
      Issue No: Vol. 864 (2019)
  • Meso-scale transport in sticky granular fluids
    • Authors: S. Luding
      Pages: 1 - 4
      Abstract: Fluid mechanics and rheology involve many unsolved challenges related to the transport mechanisms of mass, momentum and energy – especially when it comes to realistic, industrially relevant materials. Very interesting are suspensions or granular fluids with solid, particulate ingredients that feature contact mechanics on the micro-scale, which affect the transport properties on the continuum- or macro-scale. Their unique ability to behave as either fluid, or solid or both, can be quantified by non-Newtonian rheological rules, and results in interesting mechanisms such as super-diffusion, shear thickening, fluid–solid transitions (jamming) or relaxation/creep. Focusing on the steady state flow of a granular fluid, one can attempt to answer a long-standing question: how do realistic material properties such as dissipation, stiffness, friction or cohesion influence the rheology of a granular fluid' In a recent paper Macaulay & Rognon (J. Fluid Mech., vol. 858, 2019, R2) shed new light on the effect cohesion can have on mass transport in sheared, sticky granular fluids. On top of the usual diffusive, stochastic modes of transport, cohesion can create and stabilise clusters of particles into bigger agglomerates that carry particles over large distances – either ballistically in the dilute regime, or by their rotation in the dense regime. Importantly, these clusters must not only be larger than the particles (defining the intermediate, meso-scale), but they must also have a finite lifetime, in order to be able to exchange mass with each other, which can seriously enhance transport in sticky granular fluids by rotection, i.e. a combination of rotation and convection.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.34
      Issue No: Vol. 864 (2019)
  • The acoustic impedance of a laminar viscous jet through a thin circular
    • Authors: David Fabre; Raffaele Longobardi, Paul Bonnefis, Paolo Luchini
      Pages: 5 - 44
      Abstract: The unsteady axisymmetric flow through a circular aperture in a thin plate subjected to harmonic forcing (for instance under the effect of an incident acoustic wave) is a classical problem first considered by Howe (Proc. R. Soc. Lond. A, vol. 366, 1979, pp. 205–223), using an inviscid model. The purpose of this work is to reconsider this problem through a numerical resolution of the incompressible linearized Navier–Stokes equations (LNSE) in the laminar regime, corresponding to $Re=[500,5000]$ . We first compute a steady base flow which allows us to describe the vena contracta phenomenon in agreement with experiments. We then solve a linear problem allowing us to characterize both the spatial amplification of the perturbations and the impedance (or equivalently the Rayleigh conductivity), which is a key quantity to investigate the response of the jet to acoustic forcing. Since the linear perturbation is characterized by a strong spatial amplification, the numerical resolution requires the use of a complex mapping of the axial coordinate in order to enlarge the range of Reynolds number investigated. The results show that the impedances computed with $Re\gtrsim 1500$ collapse onto a single curve, indicating that a large Reynolds number asymptotic regime is effectively reached. However, expressing the results in terms of conductivity leads to substantial deviation with respect to Howe’s model. Finally, we investigate the case of finite-amplitude perturbations through direct numerical simulations (DNS). We show that the impedance predicted by the linear approach remains valid for amplitudes up to order $10^{-1}$ , despite the fact that the spatial evolution of the perturbations in the jet is strongly nonlinear.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1008
      Issue No: Vol. 864 (2019)
  • Sensitivity analysis and passive control of the secondary instability in
           the wake of a cylinder
    • Authors: F. Giannetti; S. Camarri, V. Citro
      Pages: 45 - 72
      Abstract: The stability properties of selected flow configurations, usually denoted as base flows, can be significantly altered by small modifications of the flow, which can be caused, for instance, by a non-intrusive passive control. This aspect is amply demonstrated in the literature by ad hoc sensitivity studies which, however, focus on configurations characterised by a steady base flow. Nevertheless, several flow configurations of interest are characterised by a time-periodic base flow. To this purpose, we propose here an original theoretical framework suitable to quantify the effects of base-flow variations in the stability properties of saturated time-periodic limit cycles. In particular, starting from a Floquet analysis of the linearised Navier–Stokes equations and using adjoint methods, it is possible to estimate the variation of a selected Floquet exponent caused by a generic structural perturbation of the base-flow equations. This link is expressed concisely using the adjoint operators coming from the analysis, and the final result, when applied to spatially localised disturbances, is used to build spatial sensitivity and control maps. These maps identify the regions of the flow where the placement of a infinitesimal small object produces the largest effect on the Floquet exponent and may also provide a quantification of this effect. Such analysis brings useful insights both for passive control strategies and for further characterising the investigated instability. As an example of application, the proposed analysis is applied here to the three-dimensional flow instabilities in the wake past a circular cylinder. This is a classical problem which has been widely studied in the literature. Nevertheless, by applying the proposed analysis we derive original results comprising a further characterisation of the instability and related control maps. We finally show that the control maps obtained here are in very good agreement with control experiments documented in the literature.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.17
      Issue No: Vol. 864 (2019)
  • Forced synchronization and asynchronous quenching of periodic oscillations
           in a thermoacoustic system
    • Authors: Sirshendu Mondal; Samadhan A. Pawar, R. I. Sujith
      Pages: 73 - 96
      Abstract: We perform an experimental and theoretical study to investigate the interaction between an external harmonic excitation and a self-excited oscillatory mode ( $f_{n0}$ ) of a prototypical thermoacoustic system, a horizontal Rijke tube. Such an interaction can lead to forced synchronization through the routes of phase locking or suppression. We characterize the transition in the synchronization behaviour of the forcing and the response signals of the acoustic pressure while the forcing parameters, i.e. amplitude ( $A_{f}$ ) and frequency ( $f_{f}$ ) of forcing are independently varied. Further, suppression is categorized into synchronous quenching and asynchronous quenching depending upon the value of frequency detuning ( $|\,f_{n0}-f_{f}|$ ). When the applied forcing frequency is close to the natural frequency of the system, the suppression in the amplitude of the self-excited oscillation is known as synchronous quenching. However, this suppression is associated with resonant amplification of the forcing signal, leading to an overall increase in the response amplitude of oscillations. On the other hand, an almost 80 % reduction in the root mean square value of the response oscillation is observed when the system is forced for a sufficiently large value of the frequency detuning (only for $f_{f}
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1011
      Issue No: Vol. 864 (2019)
  • Viscous fingering phenomena in the early stage of polymer membrane
    • Authors: Manuel Hopp-Hirschler; Mostafa Safdari Shadloo, Ulrich Nieken
      Pages: 97 - 140
      Abstract: Currently, the most important preparation process for porous polymer membranes is the phase inversion process. While applied for several decades in industry, the mechanism that leads to diverse morphology is not fully understood today. In this work, we present time resolved experiments using light microscopy that indicate viscous fingering during the early stage of pore formation in porous polymer membranes. Numerical simulations using the smoothed particle hydrodynamics method are also performed based on Cahn–Hilliard and Navier–Stokes equations to investigate the formation of viscous fingers in miscible and immiscible systems. The comparison of pore formation characteristics in the experiment and simulation shows that immiscible viscous fingering is present; however, it is only relevant in specific preparation set-ups similar to Hele-Shaw cells. In experiments, we also observe the formation of Liesegang rings. Enabling diffusive mass transport across the immiscible interface leads to Liesegang rings in the simulation. We conclude that further investigations of Liesegang pattern as a relevant mechanism in the formation of morphology in porous polymer membranes are necessary.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.4
      Issue No: Vol. 864 (2019)
  • Curvature-induced deformations of the vortex rings generated at the exit
           of a rectangular duct
    • Authors: Abbas Ghasemi; Burak Ahmet Tuna, Xianguo Li
      Pages: 141 - 180
      Abstract: Rectangular air jets of aspect ratio $2$ are studied at $Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$ using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ( $f_{n}$ ) and subharmonic ( $f_{n}/2$ ) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at $f_{n}/2$ shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.988
      Issue No: Vol. 864 (2019)
  • Passive scalar dispersion in the near wake of a multi-scale array of
           rectangular cylinders
    • Authors: Pawel Baj; Oliver R. H. Buxton
      Pages: 181 - 220
      Abstract: The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.11
      Issue No: Vol. 864 (2019)
  • Restricted nonlinear model for high- and low-drag events in plane channel
    • Authors: Frédéric Alizard; Damien Biau
      Pages: 221 - 243
      Abstract: A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.14
      Issue No: Vol. 864 (2019)
  • Scale invariance in finite Reynolds number homogeneous isotropic
    • Authors: L. Djenidi; R. A. Antonia, S. L. Tang
      Pages: 244 - 272
      Abstract: The problem of homogeneous isotropic turbulence (HIT) is revisited within the analytical framework of the Navier–Stokes equations, with a view to assessing rigorously the consequences of the scale invariance (an exact property of the Navier–Stokes equations) for any Reynolds number. The analytical development, which is independent of the 1941 (K41) and 1962 (K62) theories of Kolmogorov for HIT for infinitely large Reynolds number, is applied to the transport equations for the second- and third-order moments of the longitudinal velocity increment, $(\unicode[STIX]{x1D6FF}u)$ . Once the normalised equations and the constraints required for complying with the scale-invariance property of the equations are presented, results derived from these equations and constraints are discussed and compared with measurements. It is found that the fluid viscosity, $\unicode[STIX]{x1D708}$ , and the mean kinetic energy dissipation rate, $\overline{\unicode[STIX]{x1D716}}$ (the overbar denotes spatial and/or temporal averaging), are the only scaling parameters that make the equations scale-invariant. The analysis further leads to expressions for the distributions of the skewness and the flatness factor of $(\unicode[STIX]{x1D6FF}u)$ and shows that these distributions must exhibit plateaus (of different magnitudes) in the dissipative and inertial ranges, as the Taylor microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$ increases indefinitely. Also, the skewness and flatness factor of the longitudinal velocity derivative become constant as $Re_{\unicode[STIX]{x1D706}}$ increases; this is supported by experimental data. Further, the analysis, backed up by experimental evidence, shows that, beyond the dissipative range, the behaviour of $\overline{(\unicode[STIX]{x1D6FF}u)^{n}}$ with $n=2$ , 3 and 4 cannot be represented by a power law of the form
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.28
      Issue No: Vol. 864 (2019)
  • Flow-induced motions of flexible plates: fluttering, twisting and orbital
    • Authors: Yaqing Jin; Jin-Tae Kim, Shifeng Fu, Leonardo P. Chamorro
      Pages: 273 - 285
      Abstract: The unsteady dynamics of wall-mounted flexible plates under inclined flows was fundamentally described using theoretical arguments and experiments under various Cauchy numbers $Ca=\unicode[STIX]{x1D70C}_{f}bL^{3}U_{0}^{2}/(EI)\in [7,81]$ (where $\unicode[STIX]{x1D70C}_{f}$ is the fluid density, $b$ and $L$ are the plate width and length, $U_{0}$ is the incoming velocity, $E$ is Young’s modulus and $I$ is the second moment of the area) and inclination angles $\unicode[STIX]{x1D6FC}$ . Three-dimensional particle tracking velocimetry and a high-resolution force sensor were used to characterize the evolution of the plate dynamics and aerodynamic force. We show the existence of three distinctive, dominant modes of tip oscillations, which are modulated by the structure dynamic and flow instability. The first mode is characterized by small-amplitude, planar fluttering-like motions occurring under a critical Cauchy number, $Ca=Ca_{c}$ . Past this condition, the motions are dominated by the second mode consisting of unsteady twisting superimposed onto the fluttering patterns. The onset of this mode is characterized by a sharp increase of the force fluctuation intensity. At sufficiently high
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.40
      Issue No: Vol. 864 (2019)
  • Path instabilities of streamlined bodies
    • Authors: Thibault Guillet; Martin Coux, David Quéré, Christophe Clanet
      Pages: 286 - 302
      Abstract: We study the trajectory and the maximum diving depth of floating axisymmetric streamlined bodies impacting water with a vertical velocity. Three different types of underwater trajectory can be observed. For a centre of mass of the projectile located close to its leading edge, the trajectory is either straight at low velocity or y-shaped at high velocity. When the centre of mass is far from the leading edge, the trajectory has a U-shape, independent of the initial velocity. We first characterize experimentally the aerodynamic properties of the projectile and then solve the equations of motion to recover the three types of trajectories. We finally discuss the transitions between the different regimes.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1031
      Issue No: Vol. 864 (2019)
  • Mean flow generation by three-dimensional nonlinear internal wave beams
    • Authors: F. Beckebanze; K. J. Raja, L. R. M. Maas
      Pages: 303 - 326
      Abstract: We study the generation of resonantly growing mean flow by weakly nonlinear internal wave beams. With a perturbational expansion, we construct analytic solutions for three-dimensional internal wave beams, exact up to first-order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation – known as streaming – has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.22
      Issue No: Vol. 864 (2019)
  • On drag reduction scaling and sustainability bounds of superhydrophobic
           surfaces in high Reynolds number turbulent flows
    • Authors: Amirreza Rastegari; Rayhaneh Akhavan
      Pages: 327 - 347
      Abstract: The drag reduction characteristics and sustainability bounds of superhydrophobic (SH) surfaces in high Reynolds number turbulent flows are investigated using results from direct numerical simulation (DNS) and scaling-law analysis. The DNS studies were performed, using lattice Boltzmann methods, in turbulent channel flows at bulk Reynolds numbers of $Re_{b}=3600$ ( $Re_{\unicode[STIX]{x1D70F}_{0}}\approx 222$ ) and $Re_{b}=7860$ ( $Re_{\unicode[STIX]{x1D70F}_{0}}\approx 442$ ) with SH longitudinal microgrooves or SH aligned microposts on the walls. Surface microtexture geometrical parameters corresponding to microgroove widths or micropost spacings of $4\lesssim g^{+0}\lesssim 128$ in base flow wall units and solid fractions of $1/64\leqslant \unicode[STIX]{x1D719}_{s}\leqslant 1/2$ were investigated at interface protrusion angles of $\unicode[STIX]{x1D703}_{p}=0^{\circ }$ and $\unicode[STIX]{x1D703}_{p}=-30^{\circ }$ . Analysis of the governing equations and DNS results shows that the magnitude of drag reduction is not only a function of the geometry and size of the surface microtexture in wall units, but also the Reynolds number of the base flow. A Reynolds number independent measure of drag reduction can be constructed by parameterizing the magnitude of drag reduction in terms of the friction coefficient of the base flow and the shift, $(B-B_{0})$ , in the intercept of a logarithmic law representation of the mean velocity profile in the flow with SH walls compared to the base flow, where
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1027
      Issue No: Vol. 864 (2019)
  • Lagrangian transport by vertically confined internal gravity wavepackets
    • Authors: T. S. van den Bremer; H. Yassin, B. R. Sutherland
      Pages: 348 - 380
      Abstract: We examine the flows induced by horizontally modulated, vertically confined (or guided), internal wavepackets in a stratified, Boussinesq fluid. The wavepacket induces both an Eulerian flow and a Stokes drift, which together determine the Lagrangian transport of passive tracers. We derive equations describing the wave-induced flows in arbitrary stable stratification and consider four special cases: a two-layer fluid, symmetric and asymmetric piecewise constant (‘top-hat’) stratification and, more representative of the ocean, exponential stratification. In a two-layer fluid, the Stokes drift is positive everywhere with the peak value at the interface, whereas the Eulerian flow is negative and uniform with depth for long groups. Combined, the net depth-integrated Lagrangian transport is zero. If one layer is shallower than the other, the wave-averaged interface displaces into that layer making the Eulerian flow in that layer more negative and the Eulerian flow in the opposite layer more positive so that the depth-integrated Eulerian transports are offset by the same amount in each layer. By contrast, in continuous stratification the depth-integrated transport due to the Stokes drift and Eulerian flow are each zero, but the Eulerian flow is singular if the horizontal phase speed of the induced flow equals the group velocity of the wavepacket, giving rise to a single resonance in uniform stratification (McIntyre, J. Fluid Mech., vol. 60, 1973, pp. 801–811). In top-hat stratification, this single resonance disappears, being replaced by multiple resonances occurring when the horizontal group velocity of the wavepacket matches the horizontal phase speed of higher-order modes. Furthermore, if the stratification is not vertically symmetric, then the Eulerian induced flow varies as the inverse squared horizontal wavenumber for shallow waves, the same as for the asymmetric two-layer case. This ‘infrared catastrophe’ also occurs in the case of exponential stratification suggesting significant backward near-surface transport by the Eulerian induced flow for modulated oceanic internal modes. Numerical simulations are performed confirming these theoretical predictions.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.30
      Issue No: Vol. 864 (2019)
  • Resolving the horizontal direction of internal tide generation
    • Authors: Friederike Pollmann; Jonas Nycander, Carsten Eden, Dirk Olbers
      Pages: 381 - 407
      Abstract: The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.9
      Issue No: Vol. 864 (2019)
  • Dynamics of a large population of red blood cells under shear flow
    • Authors: C. Minetti; V. Audemar, T. Podgorski, G. Coupier
      Pages: 408 - 448
      Abstract: An exhaustive description of the dynamics under shear flow of a large number of red blood cells in a dilute regime is proposed, which highlights and takes into account the dispersion in cell properties within a given blood sample. Physiological suspending fluid viscosity is considered, a configuration surprisingly seldom considered in experimental studies, as well as a more viscous fluid that is a reference in the literature. Stable and unstable flipping motions well described by Jeffery orbits or modified Jeffery orbits are identified, as well as transitions to and from tank-treading motion in the more viscous suspending fluid case. Hysteresis loops upon shear rate increase or decrease are highlighted for the transitions between unstable and stable orbits as well as for the transition between flipping and tank-treading. We identify which of the characteristic parameters of motion and of the transition thresholds depend on flow stress only or also on suspending fluid viscosity.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.42
      Issue No: Vol. 864 (2019)
  • Laminar spread of a circular liquid jet impinging axially on a rotating
    • Authors: B. Scheichl; A. Kluwick
      Pages: 449 - 489
      Abstract: The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number, $Ro$ . The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by $Ro$ . Its numerical solutions are discussed for a wide range of values of $Ro$ . The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases $Ro\gg 1$ and $Ro\ll 1$ . The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1009
      Issue No: Vol. 864 (2019)
  • Condensates in thin-layer turbulence
    • Authors: Adrian van Kan; Alexandros Alexakis
      Pages: 490 - 518
      Abstract: We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.29
      Issue No: Vol. 864 (2019)
  • Penetration of boundary-driven flows into a rotating spherical thermally
           stratified fluid
    • Authors: Grace A. Cox; Christopher J. Davies, Philip W. Livermore, James Singleton
      Pages: 519 - 553
      Abstract: Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), $10^{-3}\leqslant S\leqslant 10^{4}$ , a buoyancy parameter (the strength of applied boundary heat-flux anomalies), $10^{-2}\leqslant B\leqslant 10^{6}$ , and the Ekman number (ratio of viscous to Coriolis forces), $10^{-6}\leqslant E\leqslant 10^{-4}$ . We find both steady and time-dependent solutions and delineate the regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low $S$ regime, in which buoyancy dominates the dynamics, and a high $S$ regime, in which stratification dominates. For the low- $S$ regime, we find that the characteristic flow speed scales as $B^{2/3}$ , whereas for high- $S$ , the radial and horizontal velocities scale respectively as $u_{r}\sim S^{-1}$ ,
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.999
      Issue No: Vol. 864 (2019)
  • Time-dependent lift and drag on a rigid body in a viscous steady linear
    • Authors: Fabien Candelier; Bernhard Mehlig, Jacques Magnaudet
      Pages: 554 - 595
      Abstract: We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.23
      Issue No: Vol. 864 (2019)
  • Viscoplastic water entry
    • Authors: Maziyar Jalaal; Dave Kemper, Detlef Lohse
      Pages: 596 - 613
      Abstract: The impact of viscoplastic droplets on a free surface of water is studied. The droplet undergoes an elasto-plastic deformation at the early stages of water entry. At large time, the yield stress dominates; therefore, the droplet solidifies and reaches an equilibrium shape. Depending on the impact velocity and the rheology of the droplet, the final morphologies vary from pear-shaped to capsules that contain bubbles. We perform an analysis of the orders of magnitude of the forces and introduce the relevant dimensionless groups. Furthermore, we categorize the final shapes in a phase diagram and analyse their geometrical properties. The process presents a method of making non-spherical beads and capsules with tunable shapes and provides information on the general problem of the impact of highly deformable objects on a liquid surface.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.32
      Issue No: Vol. 864 (2019)
  • Spatio-temporal proper orthogonal decomposition of turbulent channel flow
    • Authors: Srikanth Derebail Muralidhar; Bérengère Podvin, Lionel Mathelin, Yann Fraigneau
      Pages: 614 - 639
      Abstract: An extension of proper orthogonal decomposition is applied to the wall layer of a turbulent channel flow ( $Re_{\unicode[STIX]{x1D70F}}=590$ ), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the eigenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200–300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12 $u_{\unicode[STIX]{x1D70F}}$ in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.48
      Issue No: Vol. 864 (2019)
  • Multi-point Monin–Obukhov similarity in the convective atmospheric
           surface layer using matched asymptotic expansions
    • Authors: Chenning Tong; Mengjie Ding
      Pages: 640 - 669
      Abstract: The multi-point Monin–Obukhov similarity (MMO) was recently proposed (Tong & Nguyen, J. Atmos. Sci., vol. 72, 2015, pp. 4337–4348) to address the issue of incomplete similarity in the framework of the original Monin–Obukhov similarity theory (MOST). MMO hypothesizes the following: (1) The surface-layer turbulence, defined to consist of eddies that are entirely inside the surface layer, has complete similarity, which however can only be represented by multi-point statistics, requiring a horizontal characteristic length scale (absent in MOST). (2) The Obukhov length $L$ is also the characteristic horizontal length scale; therefore, all surface-layer multi-point statistics, non-dimensionalized using the surface-layer parameters, depend only on the height and separations between the points, non-dimensionalized using $L$ . However, similar to MOST, MMO was also proposed as a hypothesis based on phenomenology. In this work we derive MMO analytically for the case of the horizontal Fourier transforms of the velocity and potential temperature fluctuations, which are equivalent to the two-point horizontal differences of these variables, using the spectral forms of the Navier–Stokes and the potential temperature equations. We show that, for the large-scale motions (wavenumber $k-L$ to $z
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.38
      Issue No: Vol. 864 (2019)
  • Reduction of pressure losses and increase of mixing in laminar flows
           through channels with long-wavelength vibrations
    • Authors: J. M. Floryan; Sahab Zandi
      Pages: 670 - 707
      Abstract: Pressure losses and mixing in vibrating channels were analysed. The vibrations in the form of long-wavelength travelling waves were considered. Significant reduction of pressure losses can be achieved using sufficiently fast waves propagating downstream, while significant increase of such losses is generated by waves propagating upstream. The mechanisms responsible for pressure losses were identified and discussed. The interaction of the pressure field with the waves can create a force which assists the fluid movement. A similar force can be created by friction, but only under conditions leading to flow separation. An analysis of particle trajectories was carried out to determine the effect of vibrations on mixing. A significant transverse particle movement takes place, including particle trajectories with back loops. The downstream-propagating out-of-the phase waves provide a large reduction of pressure gradient and significant potential for mixing intensification. Analysis of energy requirements demonstrates that it is possible to identify waves which reduce power requirements, i.e. the cost of actuation is smaller than the energy savings associated with the reduction of pressure gradient. The fast forward moving waves provide an opportunity for the development of alternative propulsion methods which can be more efficient than methods based on the pressure difference.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.21
      Issue No: Vol. 864 (2019)
  • Transfer functions for flow predictions in wall-bounded turbulence
    • Authors: Kenzo Sasaki; Ricardo Vinuesa, André V. G. Cavalieri, Philipp Schlatter, Dan S. Henningson
      Pages: 708 - 745
      Abstract: Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$ , using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$ . These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.27
      Issue No: Vol. 864 (2019)
  • Perturbative corrections for the scaling of heat transport in a Hele-Shaw
           geometry and its application to geological vertical fractures
    • Authors: Juvenal A. Letelier; Nicolás Mujica, Jaime H. Ortega
      Pages: 746 - 767
      Abstract: In this work, we investigate numerically the perturbative effects of cell aperture in heat transport and thermal dissipation rate for a vertical Hele-Shaw geometry, which is used as an analogue representation of a planar vertical fracture at the laboratory scale. To model the problem, we derive a two-dimensional set of equations valid for this geometry. For Hele-Shaw cells heated from below and above, with periodic boundary conditions in the horizontal direction, the model gives new nonlinear scalings for both the time-averaged Nusselt number $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ and dimensionless mean thermal dissipation rate $\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$ in the high-Rayleigh regime. We demonstrate that $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ and $\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$ depend upon the cell anisotropy ratio $\unicode[STIX]{x1D716}$ , which measures the ratio between the cell gap and height. We show that $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ values in the high-Rayleigh regime decrease when $\unicode[STIX]{x1D716}$ grows, supporting the field observations at the fracture scale. When $\unicode[STIX]{x1D716}\ll 1$ , our results are in agreement with the scalings found using the Darcy model. The numerical results satisfy the theoretical relation $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}=Ra\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$ , which is obtained from the model. This latter relation is valid for all values of Rayleigh number considered. The perturbative eff...
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.3
      Issue No: Vol. 864 (2019)
  • The cell-free layer in simulated microvascular networks
    • Authors: Peter Balogh; Prosenjit Bagchi
      Pages: 768 - 806
      Abstract: In the microcirculation, a plasma layer forms near the vessel walls that is free of red blood cells (RBCs). This region, often termed as the cell-free layer (CFL), plays important haemorheological and biophysical roles, and has been the subject of extensive research. Many previous studies have considered the CFL development in single, isolated vessels that are straight tubes or channels, as well as in isolated bifurcations and mergers. In the body, blood vessels are typically winding and sequentially bifurcate into smaller vessels or merge to form larger vessels. Because of this geometric complexity, the CFL in vivo is three-dimensional (3D) and asymmetric, unlike in fully developed flow in straight tubes. The three-dimensionality of the CFL as it develops in a vascular network, and the underlying hydrodynamic mechanisms, are not well understood. Using a high-fidelity model of cellular-scale blood flow in microvascular networks with in vivo-like topologies, we present a detailed analysis of the fully 3D and asymmetric nature of the CFL in such networks. We show that the CFL significantly varies over different aspects of the networks. Along the vessel lengths, such variations are predominantly non-monotonic, which indicates that the CFL profiles do not simply become more symmetric over the length as they would in straight vessels. We show that vessel tortuosity causes the CFL to become more asymmetric along the length. We specifically identify a curvature-induced migration of the RBCs as the underlying mechanism of increased asymmetry in curved vessels. The vascular bifurcations and mergers are also seen to change the CFL profiles, and in the majority of them the CFL becomes more asymmetric. For most bifurcations, this is generally observed to occur such that the CFL downstream narrows on the side of the vessel nearest the upstream bifurcation, and widens on the other side. The 3D aspects of such behaviour are elucidated. For many bifurcations, a discrepancy exists between the CFL in the daughter vessels, which arises from a disproportionate partitioning between the flow rate and RBC flux. For most mergers, the downstream CFL narrows in the plane of the merger, but widens away from this plane. The dominant mechanism by which such changes occur is identified as the geometric focusing of the two merging streams. To our knowledge, this work provides the first simulation-based analysis of the 3D CFL structure in complex in vivo-like microvascular networks, including the hydrodynamic origins of the observed behaviour.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.45
      Issue No: Vol. 864 (2019)
  • Shock-induced energy conversion of entropy in non-ideal fluids
    • Authors: Emile Touber; Nicolas Alferez
      Pages: 807 - 847
      Abstract: From shaping cosmic structures in space to producing intense sounds in aircraft engines, shock waves in fluids ineluctably convert entropy fluctuations into swirling motions and sound waves. Studies of the corresponding conversion from internal energy to kinetic energy have so far been restricted to ideal (or idealised) fluids. Yet, many substances do not obey the ideal-gas law (including those in the above two examples). The present work demonstrates that non-ideal thermodynamic properties provide a remarkable degree of control over the conversion to solenoidal and dilatational kinetic energies. Of particular interest is the ability to suppress much of the emitted acoustic field whilst promoting mixing downstream of the shock. This is made possible by exploiting the convexity (or lack thereof) of the shock adiabats. Whilst illustrated here using dense vapours near the thermodynamic critical point, this ability to design and control specific shock-induced energy transfers extends beyond near-critical-point phenomena; e.g. shocked mixtures (high-speed dusty flows on Mars, nanoparticle formation in supersonic expanders for drug manufacturing), reacting fronts (supersonic combustion, rocket propulsion), ionising shocks (reentry systems, inertial confinement fusion) or fronts in active fluids (bacterial and crowd flows). This theoretical work, which demonstrates the predictive capabilities of linear theory, lays the foundation for future experimental investigations ultimately aimed at delivering novel shock-based flow-control strategies exploiting the thermodynamic properties of the fluid.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.25
      Issue No: Vol. 864 (2019)
  • Study of asymmetrical shock wave reflection in steady supersonic flow
    • Authors: Jing Lin; Chen-Yuan Bai, Zi-Niu Wu
      Pages: 848 - 875
      Abstract: The asymmetrical Mach reflection configuration is studied analytically in this paper, using an asymmetrical model extended from a recent symmetrical model and accounting for the new features related to asymmetry of the two wedges. It is found that the two sliplines do not turn parallel to the incoming flow at the same horizontal location and the sonic throat locates at the position where the difference of slopes of the two sliplines vanishes. This allows us to define a new sonic throat compatibility condition essential to determine the size of the Mach stem. The present model gives the height of the Mach stem, declined angle of the Mach stem from vertical axis, sonic throat location and shape of all shock waves and sliplines. The accuracy of the model is checked by computational fluid dynamics (CFD) simulation. It is found that the Mach stem height is strongly dependent on asymmetry of the wedge angles and almost linearly dependent on the asymmetry of the wedge lower surface lengths. The Mach stem height is shown to be insensitive to the asymmetry of the horizontal positions of the two wedges. The mechanisms for these observations are explained. For instance, it is demonstrated that the Mach reflection configuration remains closely similar when there is horizontal shift of either wedge.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.18
      Issue No: Vol. 864 (2019)
  • Experiments on wave propagation in grease ice: combined wave gauges and
           particle image velocimetry measurements
    • Authors: Jean Rabault; Graig Sutherland, Atle Jensen, Kai H. Christensen, Aleksey Marchenko
      Pages: 876 - 898
      Abstract: Water wave attenuation by grease ice is a key mechanism for the polar regions, as waves in ice influence many phenomena such as ice drift, ice breaking and ice formation. However, the models presented so far in the literature are limited in a number of regards, and more insights are required from either laboratory experiments or fieldwork for these models to be validated and improved. Unfortunately, performing detailed measurements of wave propagation in grease ice, either in the field or in the laboratory, is challenging. As a consequence, laboratory data are relatively scarce, and often consist of only a couple of wave elevation measurements along the length of the wave tank. We present combined measurements of wave elevation using an array of ultrasonic probes, and water kinematics using particle image velocimetry (PIV), in a small-scale wave tank experiment. Experiments are performed over a wider frequency range than has been previously investigated. The wave elevation measurements are used to compute the wavenumber and exponential damping coefficient. In contrast to a previous study in grease ice, we find that the wavenumber is consistent with the mass loading model, i.e. it increases compared with the open water case. Wave attenuation is compared with a series of one-layer models, and we show that they satisfactorily describe the viscous damping occurring. PIV data are also consistent with exponential wave amplitude attenuation, and a proper orthogonal decomposition analysis reveals the existence of mean flows under the ice that are a consequence of the displacement and packing of the ice induced by the gradient in the wave-induced stress. Finally, we show that the dynamics of grease ice can generate eddy structures that inject eddy viscosity into the water under the grease ice, which would lead to enhanced mixing and participating in energy dissipation.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.16
      Issue No: Vol. 864 (2019)
  • Backflow from a model fracture network: an asymptotic investigation
    • Authors: Asaf Dana; Gunnar G. Peng, Howard A. Stone, Herbert E. Huppert, Guy Z. Ramon
      Pages: 899 - 924
      Abstract: We develop a model for predicting the flow resulting from the relaxation of pre-strained, fluid-filled, elastic network structures. This model may be useful for understanding relaxation processes in various systems, e.g. deformable microfluidic systems or by-products from hydraulic fracturing operations. The analysis is aimed at elucidating features that may provide insight on the rate of fluid drainage from fracturing operations. The model structure is a bifurcating network made of fractures with uniform length and elastic modulus, which allows for general self-similar branching and variation in fracture length and rigidity between fractures along the flow path. A late-time $t^{-1/3}$ power law is attained and the physical behaviour can be classified into four distinct regimes that describe the late-time dynamics based on the location of the bulk of the fluid volume (which shifts away from the outlet as branching is increased) and pressure drop (which shifts away from the outlet as rigidity is increased upstream) along the network. We develop asymptotic solutions for each of the regimes, predicting the late-time flux and evolution of the pressure distribution. The effects of the various parameters on the outlet flux and the network’s drainage efficiency are investigated and show that added branching and a decrease in rigidity upstream tend to increase drainage time.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.39
      Issue No: Vol. 864 (2019)
  • Experimental study of inertial particles clustering and settling in
           homogeneous turbulence
    • Authors: Alec J. Petersen; Lucia Baker, Filippo Coletti
      Pages: 925 - 970
      Abstract: We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\unicode[STIX]{x1D706}}\approx 200{-}500$ , while the particle Stokes number based on the Kolmogorov scale varies between $St_{\unicode[STIX]{x1D702}}=O(1)$ and $O(10)$ . Clustering is confirmed to be most intense for $St_{\unicode[STIX]{x1D702}}\approx 1$ , but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and with sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of $St_{\unicode[STIX]{x1D702}}\approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.31
      Issue No: Vol. 864 (2019)
  • Dynamo saturation down to vanishing viscosity: strong-field and inertial
           scaling regimes
    • Authors: Kannabiran Seshasayanan; Basile Gallet
      Pages: 971 - 994
      Abstract: We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier–Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping velocity. The model can be studied down to arbitrarily low viscosity and naturally leads to the strong-field scaling regime for the magnetic energy produced above threshold: the magnetic energy is proportional to the global rotation rate and independent of the viscosity $\unicode[STIX]{x1D708}$ . Depending on the relative orientations of global rotation and large-scale sweeping, the dynamo bifurcation is either supercritical or subcritical. In the supercritical case, the magnetic energy follows the scaling law for supercritical strong-field dynamos predicted on dimensional grounds by Pétrélis & Fauve (Eur. Phys. J. B, vol. 22, 2001, pp. 271–276). In the subcritical case, the system jumps to a finite-amplitude dynamo branch. The magnetic energy obeys a magneto-geostrophic scaling law (Roberts & Soward, Annu. Rev. Fluid Mech., vol. 4, 1972, pp. 117–154), with a turbulent Elsasser number of the order of unity, where the magnetic diffusivity of the standard Elsasser number appears to be replaced by an eddy diffusivity. In the absence of global rotation, the dynamo bifurcation is subcritical and the saturated magnetic energy obeys the equipartition scaling regime. We consider both the vicinity of the dynamo threshold and the limit of large distance from threshold to put these various scaling behaviours on firm analytical ground.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.12
      Issue No: Vol. 864 (2019)
  • Non-equilibrium thermal transport and entropy analyses in rarefied cavity
    • Authors: Vishnu Venugopal; Divya Sri Praturi, Sharath S. Girimaji
      Pages: 995 - 1025
      Abstract: Thermal transport in rarefied flows far removed from thermodynamic equilibrium is investigated using kinetic-theory-based numerical simulations. Two numerical schemes – unified gas kinetic scheme (UGKS) and direct simulation Monte Carlo (DSMC) – are employed to simulate transport at different degrees of rarefaction. Lid-driven cavity flow simulations of argon gas are performed over a range of Knudsen numbers, Mach numbers and cavity shapes. Thermal transport is then characterized as a function of lid Mach number and Knudsen number for different cavity shapes. Vast deviations from the Fourier law – including thermal transport aligned along the direction of temperature gradient – are observed. Entropy implications are examined using Sackur–Tetrode and Boltzmann $H$ -theorem formulations. At low Knudsen and Mach numbers, thermal transport is shown to be amenable to both entropy formulations. However, beyond moderate Knudsen and Mach numbers, thermal transport complies only with the Boltzmann $H$ -theorem entropy statement. Two extended thermodynamic models are compared against simulation data and found to account for some of the observed non-equilibrium behaviour.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.1028
      Issue No: Vol. 864 (2019)
  • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$I$ ++++++++++++ ++++++++ ++++-dependent+rheology+to+chute+and+shear+flow+instabilities&rft.title=Journal+of+Fluid+Mechanics&rft.issn=0022-1120&,+A.+C.+Fowler&rft_id=info:doi/10.1017/jfm.2019.43">Application of the compressible $I$ -dependent rheology to chute and shear
           flow instabilities
    • Authors: J. S. Fannon; I. R. Moyles, A. C. Fowler
      Pages: 1026 - 1057
      Abstract: We consider the instability properties of dense granular flow in inclined plane and plane shear geometries as tests for the compressible inertial-dependent rheology. The model, which is a recent generalisation of the incompressible $\unicode[STIX]{x1D707}(I)$ rheology, constitutes a hydrodynamical description of dense granular flow which allows for variability in the solids volume fraction. We perform a full linear stability analysis of the model and compare its predictions to existing experimental data for glass beads on an inclined plane and discrete element simulations of plane shear in the absence of gravity. In the case of the former, we demonstrate that the compressible model can quantitatively predict the instability properties observed experimentally, and, in particular, we find that it performs better than its incompressible counterpart. For the latter, the qualitative behaviour of the plane shear instability is also well captured by the compressible model.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.43
      Issue No: Vol. 864 (2019)
  • Impingement of high-speed cylindrical droplets embedded with an air/vapour
           cavity on a rigid wall: numerical analysis
    • Authors: Wangxia Wu; Bing Wang, Gaoming Xiang
      Pages: 1058 - 1087
      Abstract: The high-speed impingement of hollow droplets embedded with a cavity has fundamental applications in various scenarios, such as in spray coating and biomedical engineering. The impingement dynamics is modulated by the wrapping medium, different from that of denser solid droplets. With air and vapour cavities, the impingement of two kinds of hollow cylindrical droplets is simulated in the present study to investigate the morphology and physical mechanisms regarding droplet and cavity dynamics. The compressible two-phase Eulerian model is used to couple with the phase transition procedure. The results detail the evolution of droplets and collapsing dynamics of the two kinds of cavities. Processes are captured in which the impinging water-hammer shock wave interacts with the cavity, and vertical liquid jets are induced to impact the embedded cavity. For the case of the air cavity, a transmitted shock wave is formed and propagates inside the cavity. The air cavities are compressively deformed and broken into a series of small cavities. Subsequently, a range of intermittent collapsing compression wavelets are generated due to the interface collapse driven by local jets. As for the vapour cavity in the saturated state, initially, once it is impacted by the impinging shock wave, it gradually shrinks accompanied by local condensation but without generation of transmitted waves. Following the first interaction between the lower and upper surfaces of the cavity, the vapour cavity undergoes continuous condensation and collapse with repeated interface fusion. The vapour cavity finally turns into liquid water blended into the surroundings, and the strong collapsing shock waves are expanded inside the droplet. The radius ratios and initial impinging speeds are chosen to analyse the variation of the collapsing time, maximum collapsing pressure and mean pressure on the rigid wall. The pressure withstood by the wall due to the collapsing cavity increases with the initial size of the cavity and initial impinging speed. The maximum local pressures in the entire fluids and the mean pressure on the wall during the collapsing of the vapour cavities are higher than those for the air cavities.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.55
      Issue No: Vol. 864 (2019)
  • A three-dimensional model of flagellar swimming in a Brinkman fluid
    • Authors: NguyenHo Ho; Karin Leiderman, Sarah Olson
      Pages: 1088 - 1124
      Abstract: We investigate three-dimensional flagellar swimming in a fluid with a sparse network of stationary obstacles or fibres. The Brinkman equation is used to model the average fluid flow where a flow-dependent term, including a resistance parameter that is inversely proportional to the permeability, captures the effects of the fibres on the fluid. To solve for the local linear and angular velocities that are coupled to the flagellar motion, we extend the method of regularized Brinkmanlets to incorporate a Kirchhoff rod, discretized as point forces and torques along a centreline. Representing a flagellum as a Kirchhoff rod, we investigate emergent waveforms for different preferred strain and twist functions. Since the Kirchhoff rod formulation allows for out-of-plane motion, in addition to studying a preferred planar sine wave configuration, we also study a preferred helical configuration. Our numerical method is validated by comparing results to asymptotic swimming speeds derived for an infinite-length cylinder propagating planar or helical waves. Similar to the asymptotic analysis for both planar and helical bending, we observe that with small amplitude bending, swimming speed is always enhanced relative to the case with no fibres in the fluid (Stokes) as the resistance parameter is increased. For regimes not accounted for with asymptotic analysis, i.e. large amplitude planar and helical bending, our model results show a non-monotonic change in swimming speed with respect to the resistance parameter; a maximum swimming speed is observed when the resistance parameter is near one. The non-monotonic behaviour is due to the emergent waveforms; as the resistance parameter increases, the swimmer becomes incapable of achieving the amplitude of its preferred configuration. We also show how simulation results of slower swimming speeds for larger resistance parameters are actually consistent with the asymptotic swimming speeds if work in the system is fixed.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.36
      Issue No: Vol. 864 (2019)
  • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D707}$ ++++++++++++ ++++++++ ++++– ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$J$ ++++++++++++ ++++++++ +++++rheology&rft.title=Journal+of+Fluid+Mechanics&rft.issn=0022-1120&">Theory for the rheology of dense non-Brownian suspensions: divergence of
           viscosities and $\unicode[STIX]{x1D707}$ – $J$ rheology
    • Authors: Koshiro Suzuki; Hisao Hayakawa
      Pages: 1125 - 1176
      Abstract: A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\unicode[STIX]{x1D711}$ is developed. The theory successfully derives the critical behaviour in the vicinity of the jamming point (volume fraction $\unicode[STIX]{x1D711}_{J}$ ), for both the pressure $P$ and the shear stress $\unicode[STIX]{x1D70E}_{xy}$ , i.e.  $P\sim \unicode[STIX]{x1D70E}_{xy}\sim \dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}^{-2}$ , where $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate, $\unicode[STIX]{x1D702}_{0}$ is the shear viscosity of the solvent and $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}=\unicode[STIX]{x1D711}_{J}-\unicode[STIX]{x1D711}>0$ is the distance from the jamming point. It also successfully describes the behaviour of the stress ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D70E}_{xy}/P$ with respect to the viscous number $J=\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}/P$ .
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.5
      Issue No: Vol. 864 (2019)
  • Viscous-fingering mechanisms under a peeling elastic sheet
    • Authors: Gunnar G. Peng; John R. Lister
      Pages: 1177 - 1207
      Abstract: We study the mechanisms affecting the viscous-fingering instability in an elastic-walled Hele-Shaw cell by considering the stability of steady states of unidirectional peeling-by-pulling and peeling-by-bending. We demonstrate that the elasticity of the wall influences the steady base state but has a negligible direct effect on the behaviour of linear perturbations, which thus behave like in the ‘printer’s instability’ with rigid walls. Moreover, the geometry of the cell can be very well approximated as a triangular wedge in the stability analysis. We identify four distinct mechanisms – surface tension acting on the horizontal and the vertical interfacial curvatures, kinematic compression in the longitudinal base flow, and the films deposited on the cell walls – that each contribute to stabilizing the system. The vertical curvature is the dominant stabilizing mechanism for small capillary numbers, but all four mechanisms have a significant effect in a large region of parameter space.
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.59
      Issue No: Vol. 864 (2019)
  • Homogeneous+Turbulence+Dynamics+(2nd+edition).+By+Pierre+Sagaut and+Claude+Cambon.+Springer,+2018.+912 pp.+ISBN:+978-3-319-73161-2+(print)+£244.50;+ISBN:+978-3-319-73162-9+(ebook)+£195.50.&rft.title=Journal+of+Fluid+Mechanics&rft.issn=0022-1120&">Book Review - Homogeneous Turbulence Dynamics (2nd edition). By Pierre
           Sagaut and Claude Cambon. Springer, 2018. 912 pp. ISBN:
           978-3-319-73161-2 (print) £244.50; ISBN: 978-3-319-73162-9 (ebook)
    • Authors: Dan Meiron
      Pages: 1208 - 1211
      PubDate: 2019-04-10T00:00:00.000Z
      DOI: 10.1017/jfm.2019.35
      Issue No: Vol. 864 (2019)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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