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Journal of Fluid Mechanics
Journal Prestige (SJR): 1.591
Citation Impact (citeScore): 3
Number of Followers: 145  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0022-1120 - ISSN (Online) 1469-7645
Published by Cambridge University Press Homepage  [369 journals]
  • Robustness of nearshore vortices
    • Authors: James C. McWilliams; Cigdem Akan, Yusuke Uchiyama
      Abstract: Coherent vortices with horizontal swirl arise spontaneously in the wave-driven nearshore surf zone. Here, a demonstration is made of the much greater robustness of coherent barotropic dipole vortices on a sloping beach in a 2D shallow-water model compared with fully 3D models either without or with stable density stratification. The explanation is that active vortex tilting and stretching or instability in 3D disrupt an initially barotropic dipole vortex. Without stratification in 3D, the vorticity retains a dipole envelope structure but is internally fragmented. With stratification in 3D, the disrupted vortex reforms as a coherent but weaker surface-intensified baroclinic dipole vortex. An implication is that barotropic or depth-integrated dynamical models of the wave-driven surf zone misrepresent an important aspect of surf-eddy behaviour.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.510
      Issue No: Vol. 850 (2018)
  • The boundary integral formulation of Stokes flows includes slender-body
    • Authors: Lyndon Koens; Eric Lauga
      Abstract: The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and computationally. Alternatively, one can solve the Stokes equations by using an appropriate distribution of flow singularities of the right strength within the boundary, a method that is particularly useful to describe the dynamics of long slender objects for which the numerical implementation of the BI representation becomes cumbersome. While the BI approach is a mathematical consequence of the Stokes equations, the singularity method involves making judicious guesses that can only be justified a posteriori. In this paper, we use matched asymptotic expansions to derive an algebraically accurate slender-body theory directly from the BI representation able to handle arbitrary surface velocities and surface tractions. This expansion procedure leads to sets of uncoupled linear equations and to a single one-dimensional integral equation identical to that derived by Keller & Rubinow (J. Fluid Mech., vol. 75, 1976, p. 705) and Johnson (J. Fluid Mech., vol. 99, 1979, p. 411) using the singularity method. Hence, we show that it is a mathematical consequence of the BI approach that the leading-order flow around a slender body can be represented using a distribution of singularities along its centreline. Furthermore, when derived from either the single-layer or the double-layer modified BI representation, general slender solutions are only possible in certain types of flow, in accordance with the limitations of these representations.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.483
      Issue No: Vol. 850 (2018)
  • The crackling sound of Leidenfrost stars
    • Authors: P. Brunet
      Pages: 1 - 4
      Abstract: Liquid drops deposited on a hot plate can experience a boiling crisis, when the vapour flux is strong enough to ensure the levitation of the drop and the relative insulation of the liquid from the solid. It is often denoted Leidenfrost effect, after the German Johann Gottlob Leidenfrost, who first reported it in 1756. While many studies have encompassed various applied issues associated with this phenomenon, aiming to control and prevent its appearance, Ma & Burton (J. Fluid Mech., vol. 846, 2018, pp. 263–291) focused on the spontaneous appearance of a standing wave at the free surface, together with temporal oscillations, making the drop adopt the shape of a star. Their far-reaching study presents exhaustive results using six different liquids with a range of different volumes and temperatures, in which they systematically extracted the drop dynamics together with the pressure fluctuations in the vapour cushion below.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.452
      Issue No: Vol. 850 (2018)
  • Toward vortex identification based on local pressure-minimum criterion in
           compressible and variable density flows
    • Authors: Jie Yao; Fazle Hussain
      Pages: 5 - 17
      Abstract: We propose a dynamical vortex definition (the ‘ $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D70C}}$ definition’) for flows dominated by density variation, such as compressible and multi-phase flows. Based on the search of the pressure minimum in a plane, $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D70C}}$ defines a vortex to be a connected region with two negative eigenvalues of the tensor $\unicode[STIX]{x1D64E}^{M}+\unicode[STIX]{x1D64E}^{\unicode[STIX]{x1D717}}$ . Here, $\unicode[STIX]{x1D64E}^{M}$ is the symmetric part of the tensor product of the momentum gradient tensor $\unicode[STIX]{x1D735}(\unicode[STIX]{x1D70C}\unicode[STIX]{x1D66A})$ and the velocity gradient tensor $\unicode[STIX]{x1D735}\unicode[STIX]{x1D66A}$ , with $\unicode[STIX]{x1D64E}^{\unicode[STIX]{x1D717}}$ denoting the symmetric part of momentum-dilatation gradient tensor $\unicode[STIX]{x1D735}(\unicode[STIX]{x1D717}\unicode[STIX]{x1D70C}\unicode[STIX]{x1D66A})$ , and $\unicode[STIX]{x1D717}\equiv \unicode[STIX]{x1D735}\boldsymbol{\cdot }\unicode[STIX]{x1D66A}$ , the dilatation rate scalar. The
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.465
      Issue No: Vol. 850 (2018)
  • Fast and slow resonant triads in the two-layer rotating shallow water
    • Authors: Alex Owen; Roger Grimshaw, Beth Wingate
      Pages: 18 - 45
      Abstract: In this paper, we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the interplay between baroclinic and barotropic dynamics in a context where there is also a geostrophic mode. In contrast to the much-studied one-layer rotating shallow water system, we find that as well as the usual slow geostrophic mode, there are now two fast waves, a barotropic mode and a baroclinic mode. This feature permits triad resonances to occur between three fast waves, with a mixture of barotropic and baroclinic modes, an aspect that cannot occur in the one-layer system. There are now also two branches of the slow geostrophic mode, with a repeated branch of the dispersion relation. The consequences are explored in a derivation of the full set of triad interaction equations, using a multiscale asymptotic expansion based on a small-amplitude parameter. The derived nonlinear interaction coefficients are confirmed using energy and enstrophy conservation. These triad interaction equations are explored, with an emphasis on the parameter regime with small Rossby and Froude numbers.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.468
      Issue No: Vol. 850 (2018)
  • Vortex–wave interaction arrays: a sustaining mechanism for the log
    • Authors: Philip Hall
      Pages: 46 - 82
      Abstract: Vortex–wave interaction theory is used to describe new kinds of localised and distributed exact coherent structures. Starting with a localised vortex–wave interaction state driven by a single inviscid wave, regular arrays of interacting vortex–wave states are investigated. In the first instance the arrays described are operational in an infinite uniform shear flow; we refer to them as ‘uniform shear vortex–wave arrays’. The basic form of the interaction remains identical to the canonical one found by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and subsequently used to describe exact coherent structures by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). Thus in each cell of a vortex–wave array a roll stress jump is induced across the critical layer of an inviscid wave riding on the streak part of the flow. The theory is extended to arbitrary shear flows using a nonlinear Wentzel–Kramers–Brillouin–Jeffreys or ray theory approach with the wave–roll–streak field operating on a shorter length scale than the mean flow. The evolution equation governing the slow dynamics of the interaction turns out to be a modified form of the well-known mean equation for a turbulent flow, and its particular form can be interpreted as a ‘closure’ between the small and large scales of the flow. If the array structure is taken to be universal, in the sense that it applies to arbitrary shear flows, then the array takes on a form which supports a logarithmic mean velocity profile trapped between what can be identified with the ‘wake region’ and a ‘buffer layer’ well known in the context of wall-bounded turbulent flows. The many similarities between the distributed structures described and wall-bounded turbulence suggest that vortex–wave arrays might be involved in the self-sustaining process supporting the log layer. The modification of the mean profile within each cell of the array leads to ‘staircase’-like streamwise velocity profiles similar to those observed experimentally in turbulent flows. The wave field supporting the ‘staircase’ is concentrated in critical layers which can be associated with the shear layer structures that have been attributed by experimentalists to be the mechanism supporting the uniform-momentum zones of the staircase.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.425
      Issue No: Vol. 850 (2018)
  • Trailing-edge flow and noise control using porous treatments
    • Authors: Syamir Alihan Showkat Ali; Mahdi Azarpeyvand, Carlos Roberto Ilário da Silva
      Pages: 83 - 119
      Abstract: This paper is concerned with the application of porous treatments as a means of flow and aerodynamic noise reduction. An extensive experimental investigation is undertaken to study the effects of flow interaction with porous media, in particular in the context of the manipulation of flow over blunt trailing edges and attenuation of vortex shedding. Comprehensive boundary layer and wake measurements have been carried out for a long flat plate with solid and porous blunt trailing edges. Unsteady velocity and surface pressure measurements have also been performed to gain an in-depth understanding of the changes to the energy–frequency content and coherence of the boundary layer and wake structures as a result of the flow interaction with a porous treatment. Results have shown that permeable treatments can effectively delay the vortex shedding and stabilize the flow over the blunt edge via mechanisms involving flow penetration into the porous medium and discharge into the near-wake region. It has also been shown that the porous treatment can effectively destroy the spanwise coherence of the boundary layer structures and suppress the velocity and pressure coherence, particularly at the vortex shedding frequency. The flow–porous scrubbing and its effects on the near-wall and large coherent structures have also been studied. The emergence of a quasi-periodic recirculating flow field inside highly permeable surface treatments has also been investigated. Finally, the paper has identified several important mechanisms concerning the application of porous treatments for aerodynamic and aeroacoustic purposes, which can help more effective and tailored designs for specific applications.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.430
      Issue No: Vol. 850 (2018)
  • Direct numerical simulation of wind turbulence over breaking waves
    • Authors: Zixuan Yang; Bing-Qing Deng, Lian Shen
      Pages: 120 - 155
      Abstract: We study wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows. In the DNS, the air and water are simulated as a coherent system, with the interface captured using the coupled level-set and volume-of-fluid method. Because the wave breaking is an unsteady process, we use ensemble averaging over 100 runs to define turbulence statistics. We focus on analysing the turbulence statistics of the airflow over breaking waves. The effects of wave age and wave steepness are investigated. It is found that before wave breaking, the turbulence statistics are largely influenced by the wave age. The vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave age as the pressure force changes from drag to thrust. Furthermore, wave-coherent motions make increasingly important contributions to the momentum flux and kinetic energy of velocity fluctuations (KE-F) as the wave age increases. During the wave breaking process, spilling breakers do not influence the wind field significantly; in contrast, plunging breakers alter the structures of wind turbulence near the wave surface drastically. It is observed from the DNS results that during wave plunging, a high pressure region occurs ahead of the wave front, which further accelerates the wind in the downstream direction. Meanwhile, a large spanwise vortex is generated, which greatly disturbs the airflow around it, resulting in large magnitudes of Reynolds stress and turbulence kinetic energy (TKE) below the wave crest. Above the crest, the magnitude of KE-F is enhanced during wave plunging at small and large wave ages, but at intermediate wave age, the transient enhancement of KE-F is absent. The effect of wave breaking on the magnitude of KE-F is further investigated through the analysis of the KE-F production. It is discovered that at small wave age, the transient enhancement of KE-F is caused by the appearance of a local maximum in the profile of total momentum flux; but at large wave age, it results from the change in the sign of the KE-F production from negative to positive, due to the sign change in the wave-coherent momentum flux. At intermediate wave age, neither of these two processes is present, and the transient growth of KE-F does not take place.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.466
      Issue No: Vol. 850 (2018)
  • Large-eddy simulation of laminar transonic buffet
    • Authors: Julien Dandois; Ivan Mary, Vincent Brion
      Pages: 156 - 178
      Abstract: A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number $M=0.735$ , an angle of attack $\unicode[STIX]{x1D6FC}=4^{\circ }$ , a Reynolds number $Re_{c}=3\times 10^{6}$ has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies ( $St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$ , where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency ( $St=1.2$ ). The shock oscillation amplitude is also lower: 6 % of chord and limited to the shock foot area in the laminar case instead of 20 % with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.470
      Issue No: Vol. 850 (2018)
  • The evolution of a front in turbulent thermal wind balance. Part 1. Theory
    • Authors: Matthew N. Crowe; John R. Taylor
      Pages: 179 - 211
      Abstract: Here, we examine the influence of small-scale turbulence on the evolution of fronts in the ocean and atmosphere. Specifically, we consider the evolution of an initially balanced density front subject to an imposed viscosity and diffusivity as a simple analogue for small-scale turbulence. At late times, the dominant balance is found to be the quasisteady turbulent thermal wind balance with time evolution due to an advection–diffusion balance in the buoyancy equation. We use the leading-order balance to determine analytical similarity solutions for the spreading of a front and find that the spreading rate is maximum for an intermediate value of the Ekman number, with the spreading resulting from shear dispersion associated with the cross-front flow and vertical diffusion of density. In response to shear dispersion, the front evolves towards a density profile that is nearly linear in the cross-front coordinate. At the edges of the frontal zone, the density field develops large curvature, and these regions are associated with narrow bands of intense vertical velocity.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.448
      Issue No: Vol. 850 (2018)
  • Aeroacoustics of a rotor ingesting a planar boundary layer at high thrust
    • Authors: Henry H. Murray; William J. Devenport, W. Nathan Alexander, Stewart A. L. Glegg, David Wisda
      Pages: 212 - 245
      Abstract: Aeroacoustic measurements and analysis have been made for an unshrouded rotor partially immersed in a planar equilibrium turbulent boundary layer at low Mach number. This configuration provides an idealized model of inflow distortion effects seen when a rotor is mounted adjacent to the hull or fuselage of a vehicle. At low and moderate thrust conditions, the rotor produces broadband noise organized into haystacks produced by large eddies of the ingested turbulence being cut multiple times by successive rotor blades. At high thrust, however, the acoustic signature changes and becomes louder and more tonal. This change is accompanied by separation of the boundary layer from the wall in the vicinity of the rotor blade disk. The separation region is highly unsteady and populated by intense vortex structures. Acoustic analysis suggests that blade–vortex interactions with these structures are the source of the additional tonal noise at high thrust.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.438
      Issue No: Vol. 850 (2018)
  • Finite-sized rigid spheres in turbulent Taylor–Couette flow: effect
           on the overall drag
    • Authors: Dennis Bakhuis; Ruben A. Verschoof, Varghese Mathai, Sander G. Huisman, Detlef Lohse, Chao Sun
      Pages: 246 - 261
      Abstract: We report on the modification of drag by neutrally buoyant spherical finite-sized particles in highly turbulent Taylor–Couette (TC) flow. These particles are used to disentangle the effects of size, deformability and volume fraction on the drag, and are contrasted to the drag in bubbly TC flow. From global torque measurements, we find that rigid spheres hardly decrease or increase the torque needed to drive the system. The size of the particles under investigation has a marginal effect on the drag, with smaller diameter particles showing only slightly lower drag. Increase of the particle volume fraction shows a net drag increase. However, this increase is much smaller than can be explained by the increase in apparent viscosity due to the particles. The increase in drag for increasing particle volume fraction is corroborated by performing laser Doppler anemometry, where we find that the turbulent velocity fluctuations also increase with increasing volume fraction. In contrast to rigid spheres, for bubbles, the effective drag reduction also increases with increasing Reynolds number. Bubbles are also much more effective in reducing the overall drag.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.462
      Issue No: Vol. 850 (2018)
  • Toward design of the antiturbulence surface exhibiting maximum drag
           reduction effect
    • Authors: V. Krieger; R. Perić, J. Jovanović, H. Lienhart, A. Delgado
      Pages: 262 - 303
      Abstract: The flow development in a groove-modified channel consisting of flat and grooved walls was investigated by direct numerical simulations based on the Navier–Stokes equations at a Reynolds number of $5\times 10^{3}$ based on the full channel height and the bulk velocity. Simulations were performed for highly disturbed initial flow conditions leading to the almost instantaneous appearance of turbulence in channels with flat walls. The surface morphology was designed in the form of profiled grooves aligned with the flow direction and embedded in the wall. Such grooves are presumed to allow development of only the statistically axisymmetric disturbances. In contrast to the rapid production of turbulence along a flat wall, it was found that such development was suppressed over a grooved wall for a remarkably long period of time. Owing to the difference in the flow structure, friction drag over the grooved wall was more than 60 % lower than that over the flat wall. Anisotropy-invariant mapping supports the conclusion, emerging from analytic considerations, that persistence of the laminar regime is due to statistical axisymmetry in the velocity fluctuations. Complementary investigations of turbulent drag reduction in grooved channels demonstrated that promotion of such a state across the entire wetted surface is required to stabilize flow and prevent transition and breakdown to turbulence. To support the results of numerical investigations, measurements in groove-modified channel flow were performed. Comparisons of the pressure differentials measured along flat and groove-modified channels reveal a skin-friction reduction as large as $\text{DR}\approx 50\,\%$ owing to the extended persistence of the laminar flow compared with flow development in a flat channel. These experiments demonstrate that early stabilization of the laminar boundary layer development with a grooved surface promotes drag reduction in a fully turbulent flow with a preserving magnitude as the Reynolds number increases.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.423
      Issue No: Vol. 850 (2018)
  • Independent caudal fin actuation enables high energy extraction and
           control in two-dimensional fish-like group swimming
    • Authors: Amy Gao; Michael S. Triantafyllou
      Pages: 304 - 335
      Abstract: We study through numerical simulation the optimal hydrodynamic interactions and basic vorticity control mechanisms for two fish-like bodies swimming in tandem. We show that for a fish swimming in the wake of an upstream fish, using independent pitch control of its caudal fin, in addition to optimized body motion, results in reduction of the energy needed for self-propulsion by more than 50 %, providing a quasi-propulsive efficiency of 90 %, up from 60 % without independent caudal fin control. Such high efficiency is found over a narrow parametric range and is possible only when the caudal fin is allowed to pitch independently from the motion of the main body. We identify the vorticity control mechanisms employed by the body and tail to achieve this remarkable performance through thrust augmentation and destructive interference with the upstream fish-generated vortices. A high sensitivity of the propulsive performance to small variations in caudal fin parameters is found, underlying the importance of accurate flow sensing and feedback control. We further demonstrate that using lateral line-like flow measurements to drive an unscented Kalman filter, the near-field vortices can be localized within 1 % of the body length, and be used with a phase-lock controller to drive the body and tail undulation of a self-propelled fish, moving within the wake of an upstream fish, to stably reach the optimal gait and fully achieve maximum energy extraction.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.456
      Issue No: Vol. 850 (2018)
  • A direct comparison of particle-resolved and point-particle methods in
           decaying turbulence
    • Authors: M. Mehrabadi; J. A. K. Horwitz, S. Subramaniam, A. Mani
      Pages: 336 - 369
      Abstract: We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with solid-phase volume fraction $\unicode[STIX]{x1D719}=0.001$ in a decaying isotropic turbulent particle-laden flow. The particle diameter $d_{p}$ in the suspension is chosen to be the same as the initial Kolmogorov length scale $\unicode[STIX]{x1D702}_{0}$ ( $d_{p}/\unicode[STIX]{x1D702}_{0}=1$ ) in order to overlap with the regime where PP-DNS is valid. We assess the point-particle acceleration model for two different particle Stokes numbers, $St_{\unicode[STIX]{x1D702}}=1$ and 100. For the high Stokes number case, the Stokes drag model for particle acceleration under-predicts the true particle acceleration. In addition, second moment quantities which play key roles in the physical evolution of the gas–solid suspension are not correctly captured. Considering finite Reynolds number corrections to the acceleration model improves the prediction of the particle acceleration probability density function and second moment statistics of the point-particle model compared with the particle-resolved simulation. We also find that accounting for the undisturbed fluid velocity in the acceleration model can be of greater importance than using the most appropriate acceleration model for a given physical problem.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.442
      Issue No: Vol. 850 (2018)
  • Dynamics and excitation in a low mass-damping cylinder in cross-flow
           with side-by-side interference
    • Authors: Francisco J. Huera-Huarte
      Pages: 370 - 400
      Abstract: Experiments have been conducted with a low mass-damping circular cylinder, elastically supported in a cross-flow, in the vicinity of a second stationary cylinder. The dynamic response, including amplitudes and frequencies of oscillation, together with the fluid excitation, were measured covering a large parametric space, consisting of variations in the gap distance between the cylinders as well as in the reduced velocity and Reynolds number. The flow dynamics in the near wake was also measured using planar particle image velocimetry. The results show how there is a strong wake interaction between the cylinders that greatly modifies the vortex-induced vibrations (VIV) of the elastically mounted cylinder when the centre-to-centre distance between the models is initially set to values smaller than $3.5D$ , where $D$ is the external diameter. The wake interference leads to responding amplitudes that are reduced if compared to those of isolated cylinders undergoing VIV, while responding frequencies are increased. The transverse force coefficients observed in the lock-in region increase and the upper branch shifts to smaller reduced velocities. The phase between motion and excitation is also shifted and values measured in the lower branch of the response tend to be smaller than those typical of isolated cylinders. At the smallest separation distances investigated, the wakes of the cylinders are synchronised in an out-of-phase mode of shedding, characterised by a biased flow towards the oscillating cylinder.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.469
      Issue No: Vol. 850 (2018)
  • Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds
    • Authors: Xi Chen; Fazle Hussain, Zhen-Su She
      Pages: 401 - 438
      Abstract: We present new scaling expressions, including high-Reynolds-number ( $Re$ ) predictions, for all Reynolds stress components in the entire flow domain of turbulent channel and pipe flows. In Part 1 (She et al., J. Fluid Mech., vol. 827, 2017, pp. 322–356), based on the dilation symmetry of the mean Navier–Stokes equation a four-layer formula of the Reynolds shear stress length $\ell _{12}$ – and hence also the entire mean velocity profile (MVP) – was obtained. Here, random dilations on the second-order balance equations for all the Reynolds stresses (shear stress $-\overline{u^{\prime }v^{\prime }}$ , and normal stresses $\overline{u^{\prime }u^{\prime }}$ , $\overline{v^{\prime }v^{\prime }}$ , $\overline{w^{\prime }w^{\prime }}$ ) are analysed layer by layer, and similar four-layer formulae of the corresponding stress length functions $\ell _{11}$ , $\ell _{22}$ , $\ell _{33}$ (hence the three turbulence intensities) are obtained for turbulent channel and pipe flows. In particular, direct numerical simulation (DNS) data are shown to agree well with the four-layer formulae for
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.405
      Issue No: Vol. 850 (2018)
  • Heat or mass transport from drops in shearing flows. Part 1. The
           open-streamline regime
    • Authors: Deepak Krishnamurthy; Ganesh Subramanian
      Pages: 439 - 483
      Abstract: We study the heat or mass transfer from a neutrally buoyant spherical drop embedded in an ambient Newtonian medium, undergoing a general shearing flow, in the strong convection limit. The latter limit corresponds to the drop Péclet number being large ( $Pe\gg 1$ ). We consider two families of ambient linear flows: (i) planar linear flows with open streamlines (parametrized by $\unicode[STIX]{x1D6FC}$ with $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 1$ , the extremal members being simple shear flow ( $\unicode[STIX]{x1D6FC}=0$ ) and planar extension ( $\unicode[STIX]{x1D6FC}=1$ )) and (ii) three-dimensional extensional flows (parameterized by $\unicode[STIX]{x1D716}$ , with $0\leqslant \unicode[STIX]{x1D716}\leqslant 1$ , the extremal members being planar ( $\unicode[STIX]{x1D716}=0$ ) and axisymmetric extension ( $\unicode[STIX]{x1D716}=1$ )). For the first family, an analysis of the exterior flow field in the inertialess limit (the drop Reynolds number, $Re$ , being vanishingly small) shows that there ...
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.439
      Issue No: Vol. 850 (2018)
  • Heat or mass transport from drops in shearing flows. Part 2. Inertial
           effects on transport
    • Authors: Deepak Krishnamurthy; Ganesh Subramanian
      Pages: 484 - 524
      Abstract: We analyse the singular effects of weak inertia on the heat (or equivalently mass) transport problem from drops in linear shearing flows. For small spherical drops embedded in hyperbolic planar linear flows, which constitute a one-parameter family (the parameter being $\unicode[STIX]{x1D6FC}$ with $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 1$ , and whose extremal members are simple shear ( $\unicode[STIX]{x1D6FC}=0$ ) and planar extension ( $\unicode[STIX]{x1D6FC}=1$ )), there are two distinct regimes for scalar (heat or mass) transport at large Péclet numbers ( $Pe$ ) depending on the exterior streamline topology (Krishnamurthy & Subramanian, J. Fluid Mech., vol. 850, 2018, pp. 439–483). When the drop-to-medium viscosity ratio ( $\unicode[STIX]{x1D706}$ ) is larger than a critical value, $\unicode[STIX]{x1D706}_{c}=2\unicode[STIX]{x1D6FC}/(1-\unicode[STIX]{x1D6FC})$ , the drop is surrounded by a region of closed streamlines in the inertialess limit ( $Re=0$ , $Re$ being the drop Reynolds number). Convection is incapable of transporting heat away on account of the near-field closed streamline topology, and the transport remains diffusion limited even for
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.481
      Issue No: Vol. 850 (2018)
  • Bistability of buoyancy-driven exchange flows in vertical tubes
    • Authors: Jenny Suckale; Zhipeng Qin, Davide Picchi, Tobias Keller, Ilenia Battiato
      Pages: 525 - 550
      Abstract: Buoyancy-driven exchange flows are common to a variety of natural and engineering systems, ranging from persistently active volcanoes to counterflows in oceanic straits. Laboratory experiments of exchange flows have been used as surrogates to elucidate the basic features of such flows. The resulting data have been analysed and interpreted mostly through core–annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we demonstrate that some of the variability observed in laboratory experiments and natural systems is a consequence of the inherent bistability of core–annular flow. Using a core–annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes, we identify two mathematically valid solutions at steady state: a solution with fast flow in a thin core and a solution with relatively slow flow in a thick core. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Through direct numerical simulations, we confirm the hypothesis that core–annular flow in vertical tubes is inherently bistable. Our simulations suggest that the bistability of core–annular flow is linked to the boundary conditions of the domain, which implies that is not possible to predict the realized flow field from the material parameters of the fluids and the tube geometry alone. Our finding that buoyancy-driven exchange flows are inherently bistable systems is consistent with previous experimental data, but is in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. Our results have important implications for data interpretation by analytical models and may also have interesting ramifications for understanding volcanic degassing.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.382
      Issue No: Vol. 850 (2018)
  • Formation of surface trailing counter-rotating vortex pairs downstream of
           a sonic jet in a supersonic cross-flow
    • Authors: Mingbo Sun; Zhiwei Hu
      Pages: 551 - 583
      Abstract: Direct numerical simulations were conducted to uncover physical aspects of a transverse sonic jet injected into a supersonic cross-flow at a Mach number of 2.7. Simulations were carried out for two different jet-to-cross-flow momentum flux ratios ( $J$ ) of 2.3 and 5.5. It is identified that collision shock waves behind the jet induce a herringbone separation bubble in the near-wall jet wake and a reattachment valley is formed and embayed by the herringbone recirculation zone. The recirculating flow in the jet leeward separation bubble forms a primary trailing counter-rotating vortex pair (TCVP) close to the wall surface. Analysis on streamlines passing the separation region shows that the wing of the herringbone separation bubble serves as a micro-ramp vortex generator and streamlines acquire angular momentum downstream to form a secondary surface TCVP in the reattachment valley. Herringbone separation wings disappear in the far field due to the cross-interaction of lateral supersonic flow and the expansion flow in the reattachment valley, which also leads to the vanishing of the secondary TCVP. A three-dimensional schematic of surface trailing wakes is presented and explains the formation mechanisms of the surface TCVPs.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.455
      Issue No: Vol. 850 (2018)
  • Spatial modulations of kinetic energy in the roughness sublayer
    • Authors: Jérémy Basley; Laurent Perret, Romain Mathis
      Pages: 584 - 610
      Abstract: High-Reynolds-number experiments are conducted in the roughness sublayer of a turbulent boundary layer developing over a cubical canopy. Stereoscopic particle image velocimetry is performed in a wall-parallel plane to evidence a high degree of spatial modulation of the small-scale turbulence around the footprint of large-scale motions, despite the suppression of the inner layer by the high roughness elements. Both Fourier and wavelets analyses show that the near-wall cycle observed in smooth-wall-bounded flows is severely disrupted by the canopy, whose wake in the roughness sublayer generates a new range of scales, closer to that of the outer-layer large-scale motions. This restricts significantly scale separation, hence a diagnostic method is developed to divide carefully and rationally the fluctuating velocity fields into large- and small-scale components. Our analysis across all turbulent kinetic energy terms sheds light on the spatial imprint of the modulation mechanism, revealing a very different signature on each velocity component. The roughness sublayer shows a preferential arrangement of the modulated scales similar to what is observed in the outer layer of smooth-wall-bounded flows – small-scale turbulence is enhanced near the front of high momentum regions and damped at the front of low momentum regions. More importantly, accessing spanwise correlations reveals that modulation intensifies the most along the flanks of the large-scale motions.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.458
      Issue No: Vol. 850 (2018)
  • Cavity ripple dynamics after pinch-off
    • Authors: Jean-François Louf; Brian Chang, Javad Eshraghi, Austin Mituniewicz, Pavlos P. Vlachos, Sunghwan Jung
      Pages: 611 - 623
      Abstract: During water entry, a projectile can entrain an air cavity that trails behind it. Most previous studies focus on the formation and pinch-off dynamics of the air cavity, but only a few have investigated the long-term cavity dynamics after pinch-off. In this study, we examine the ripple formation following the pinch-off of an air cavity generated by a cone, with different cone angles and impact velocities. The amplitude and wavelength of these ripples are measured, and the force on the cone is experimentally determined. It was observed that the ripple amplitude and wavelength increase linearly with the cone impact velocity, which is predicted by our acoustic model of the compressible air cavity. In addition, the measured force exhibits distinct amplitudes and wavelengths. By measuring the length of the cavity, the resulting pressure variation was averaged inside the air cavity leading to a theoretical force amplitude, which matched our observations. We noted that the force wavelength also follows the same acoustic model, which agrees very well with the wavelength of the ripples.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.459
      Issue No: Vol. 850 (2018)
  • Energy flux enhancement, intermittency and turbulence via Fourier triad
           phase dynamics in the 1-D Burgers equation
    • Authors: Brendan P. Murray; Miguel D. Bustamante
      Pages: 624 - 645
      Abstract: We present a theoretical and numerical study of Fourier-space triad phase dynamics in the one-dimensional stochastically forced Burgers equation at Reynolds number $Re\approx 2.7\times 10^{4}$ . We demonstrate that Fourier triad phases over the inertial range display a collective behaviour characterised by intermittent periods of synchronisation and alignment, reminiscent of the Kuramoto model (Chemical Oscillations, Waves, and Turbulence, Springer, 1984) and directly related to collisions of shocks in physical space. These periods of synchronisation favour efficient energy fluxes across the inertial range towards small scales, resulting in strong bursts of dissipation and enhanced coherence of the Fourier energy spectrum. The fast time scale of the onset of synchronisation relegates energy dynamics to a passive role: this is further examined using a reduced system with the Fourier amplitudes fixed in time – a phase-only model. We show that intermittent triad phase dynamics persists without amplitude evolution and we broadly recover many of the characteristics of the full Burgers system. In addition, for both full Burgers and phase-only systems the physical-space velocity statistics reveals that triad phase alignment is directly related to the non-Gaussian statistics typically associated with structure-function intermittency in turbulent systems.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.454
      Issue No: Vol. 850 (2018)
  • Wake of super-hydrophobic falling spheres: influence of the air layer
    • Authors: Marco Castagna; Nicolas Mazellier, Azeddine Kourta
      Pages: 646 - 673
      Abstract: We report an experimental investigation of the wake of free falling super-hydrophobic spheres. The mutual interaction between the air layer (plastron) encapsulating the super-hydrophobic spheres and the flow is emphasised by studying the hydrodynamic performance. It is found that the air plastron adapts its shape to the flow-induced stresses which compete with the surface tension. This competition is characterised by introducing the Weber number ${\mathcal{W}}e$ , whilst the plastron deformation is estimated via the aspect ratio $\unicode[STIX]{x1D712}$ . While noticeable distortions are locally observed, the plastron becomes more and more spherical on average (i.e.  $\unicode[STIX]{x1D712}\rightarrow 1$ ) as far as ${\mathcal{W}}e$ increases. The study of the falling motion reveals that the plastron compliance has a sizeable influence on the wake development. Investigating the lift force experienced by the super-hydrophobic spheres, the onset of wake instabilities is found to be triggered earlier than for smooth spheres used as reference. Surprisingly, it is also observed that the early promotion of the wake instabilities is even more pronounced beyond a critical Weber number, ${\mathcal{W}}e_{c}$ , which corresponds to a critical aspect ratio $\unicode[STIX]{x1D712}_{c}$ . Furthermore, the magnitude of the hydrodynamic loads is found to be dependent on the average deformation of the gas/liquid interface. Indeed, in comparison to the reference spheres, the high deformation achieved for $\unicode[STIX]{x1D712}>\unicode[STIX]{x1D712}_{c}$ (oblate shape) leads to lift and drag increase, whereas the low deformation obtained for $\unicode[STIX]{x1D712}
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.480
      Issue No: Vol. 850 (2018)
  • Asymptotic scaling laws and semi-similarity solutions for a finite-source
           spherical blast wave
    • Authors: Y. Ling; S. Balachandar
      Pages: 674 - 707
      Abstract: A spherical blast wave generated by a sudden release of a sphere of compressed gas is an important model problem to understand blast phenomena such as volcanic eruptions and explosive detonations. The resulting explosion flow physics, such as the instability at the gas contact discontinuity and the interaction between the shock wave and the gas contact, are dictated by the initial pressure and sound-speed ratios between the compressed gas and the ambience. Since the initial pressure and sound-speed ratios vary over a wide range in practical applications, it is of interest to investigate the scaling laws and similarity solutions for the spherical symmetric explosion flow. In the present study, numerical simulation of a spherical blast wave is performed. A long-term length scale that incorporates the initial charge radius and the initial pressure ratio is introduced. The trajectories of the main shock normalized by the long-term length scale for a wide range of parameters collapse after a short transition time, indicating an asymptotic similarity solution exists for the far field in the long term. With the assistance of this similarity solution, the full evolution of the main shock can be obtained semi-analytically. For near-field features, i.e. the gas contact and the secondary shock wave, only semi-similarity solutions are observed, which depend on the initial sound-speed ratio but not the initial pressure ratio. The gas contact and the secondary shock share the same scaling relations. Asymptotic analysis is performed to obtain the short-term dynamics of the gas contact, including the gas contact acceleration and the Atwood number, which are the key parameters determining the Rayleigh–Taylor instability development at the gas contact. The asymptotic contact radius as $t\rightarrow \infty$ is also obtained, which is found to be well represented by the long-term length scale and thus only depends on the initial pressure ratio. A simple model of an oscillating bubble is employed to explain the scaling relation of the asymptotic gas contact radius.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.475
      Issue No: Vol. 850 (2018)
  • Topography of the lubrication film under a pancake droplet travelling in a
           Hele-Shaw cell
    • Authors: Benjamin Reichert; Axel Huerre, Olivier Theodoly, Marie-Pierre Valignat, Isabelle Cantat, Marie-Caroline Jullien
      Pages: 708 - 732
      Abstract: Understanding the dynamics of a droplet pushed by an external fluid in a confined geometry calls for the identification of all the dissipation mechanisms at play in the lubrication film between droplet and cell wall. Experimentally, reflection interference contrast microscopy has proven an efficient tool to measure the thickness of such lubrication films for microfluidic droplets, with a precision of a few nanometres (Huerre et al., Lab on a Chip, vol. 16 (5), 2016, pp. 911–916). The present work takes advantage of the high accuracy of this technique to chart quantitatively the lubrication film between oil droplets and the glass wall of a microfluidic chamber. We find that the lubrication films exhibit a complex three-dimensional shape, which we are able to rationalize using a hydrodynamical model in the lubrication approximation. We show that the complete topography cannot be recovered using a single model boundary condition along the whole interface. Rather, surface tension gradients are negligible at the front of the droplet, whereas they significantly modify the film profile at the rear, where surfactant accumulation induces local thickening of the lubrication film. The presence of ravines on the sides of the droplet is due to three-dimensional effects which can be qualitatively reproduced numerically. To our knowledge, this is the first experimental investigation of such local effects on travelling droplets.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.457
      Issue No: Vol. 850 (2018)
  • Large-scale structures in a turbulent channel flow with a minimal
           streamwise flow unit
    • Authors: Hiroyuki Abe; Robert Anthony Antonia, Sadayoshi Toh
      Pages: 733 - 768
      Abstract: Direct numerical simulations are used to examine large-scale motions with a streamwise length $2\sim 4h$ ( $h$ denotes the channel half-width) in the logarithmic and outer regions of a turbulent channel flow. We test a minimal ‘streamwise’ flow unit (Toh & Itano, J. Fluid Mech., vol. 524, 2005, pp. 249–262) (or MSU) for larger Kármán numbers ( $h^{+}=395$ and 1020) than in the original work. This flow unit consists of a sufficiently long ( ${L_{x}}^{+}\approx 400$ ) streamwise domain to maintain near-wall turbulence (Jiménez & Moin, J. Fluid Mech., vol. 225, 1991, pp. 213–240) and a spanwise domain which is large enough to represent the spanwise behaviour of inner and outer structures correctly; as $h^{+}$ increases, the streamwise extent of the MSU domain decreases with respect to $h$ . Particular attention is given to whether the spanwise organization of the large-scale structures may be represented properly in this simplified system at sufficiently large $h^{+}$ and how these structures are associated with the mean streamwise velocity $\overline{U}$ . It is shown that, in the MSU, the large-scale structures become approximately two-dimensional at $h^{+}=1020$ . In this case, the streamwise velocity fluctuation
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.434
      Issue No: Vol. 850 (2018)
  • Direct measurement of selective evaporation of binary mixture droplets by
           dissolving materials
    • Authors: Hyoungsoo Kim; Howard A. Stone
      Pages: 769 - 783
      Abstract: We investigate experimentally and theoretically how a droplet of a binary mixture evaporates when placed on a solid substrate. Our focus is the limit at which the two liquid components have different vapour pressures. Using physicochemical effects, we directly visualize the selective evaporation of the more volatile component and so document the space and time dependence of the chemical distribution in the droplet. In particular, we observe that a mixture consisting of an organic solvent and deionized water dissolves suspended fluorescent polystyrene particles if the lower volatility organic solvent reaches a critical concentration. Consequently, we show that for a small contact angle ( $\unicode[STIX]{x1D703}
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.472
      Issue No: Vol. 850 (2018)
  • Role of Darrieus–Landau instability in propagation of expanding
           turbulent flames
    • Authors: Sheng Yang; Abhishek Saha, Zirui Liu, Chung K. Law
      Pages: 784 - 802
      Abstract: In this paper we study the essential role of Darrieus–Landau (DL), hydrodynamic, cellular flame-front instability in the propagation of expanding turbulent flames. First, we analyse and compare the characteristic time scales of flame wrinkling under the simultaneous actions of DL instability and turbulent eddies, based on which three turbulent flame propagation regimes are identified, namely, instability dominated, instability–turbulence interaction and turbulence dominated regimes. We then perform experiments over an extensive range of conditions, including high pressures, to promote and manipulate the DL instability. The results clearly demonstrate the increase in the acceleration exponent of the turbulent flame propagation as these three regimes are traversed from the weakest to the strongest, which are respectively similar to those of the laminar cellularly unstable flame and the turbulent flame without flame-front instability, and thus validating the scaling analysis. Finally, based on the scaling analysis and the experimental results, we propose a modification of the conventional turbulent flame regime diagram to account for the effects of DL instability.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.426
      Issue No: Vol. 850 (2018)
  • Turbulence of capillary waves forced by steep gravity waves
    • Authors: M. Berhanu; E. Falcon, L. Deike
      Pages: 803 - 843
      Abstract: We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in the laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2–0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from the large scale to the small scale. Analysis of temporal fluctuations of the spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to the small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of the wave spectra are found to be in agreement with those of the weakly nonlinear wave turbulence theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with wave turbulence theory. These results suggest that theoretical developments beyond the classic wave turbulence theory are necessary to describe the dynamics and statistics of capillary waves in a natural environment. In particular, in the presence of broad-scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions should be reconsidered.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.467
      Issue No: Vol. 850 (2018)
  • Robustness of vortex populations in the two-dimensional inverse energy
    • Authors: B. H. Burgess; R. K. Scott
      Pages: 844 - 874
      Abstract: We study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant $A^{-1}$ scaling. We also study the impact of the forcing Reynolds number $Re_{f}$ , a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As $Re_{f}$ decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small $Re_{f}$ , and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher $Re_{f}$ . At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher $Re_{f}$ . Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.473
      Issue No: Vol. 850 (2018)
  • Optimal mixing in three-dimensional plane Poiseuille flow at high
           Péclet number
    • Authors: L. Vermach; C. P. Caulfield
      Pages: 875 - 923
      Abstract: We consider a passive zero-mean scalar field organised into two layers of different concentrations in a three-dimensional plane channel flow subjected to a constant along-stream pressure gradient. We employ a nonlinear direct-adjoint-looping method to identify the optimal initial perturbation of the velocity field with given initial energy which yields ‘maximal’ mixing by a target time horizon, where maximal mixing is defined here as the minimisation of the spatially integrated variance of the concentration field. We verify in three-dimensional flows the conjecture by Foures et al. (J. Fluid Mech., vol. 748, 2014, pp. 241–277) that the initial perturbation which maximises the time-averaged energy gain of the flow leads to relatively weak mixing, and is qualitatively different from the optimal initial ‘mixing’ perturbation which exploits classical Taylor dispersion. We carry out the analysis for two different Reynolds numbers ( $Re=U_{m}h/\unicode[STIX]{x1D708}=500$ and $Re=3000$ , where $U_{m}$ is the maximum flow speed of the unperturbed flow, $h$ is the channel half-depth and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the fluid) demonstrating that this key finding is robust with respect to the transition to turbulence. We also identify the initial perturbations that minimise, at chosen target times, the ‘mix-norm’ of the concentration field, i.e. a Sobolev norm of negative index in the class introduced by Mathew et al. (Physica D, vol. 211, 2005, pp. 23–46). We show that the ‘true’ variance-based mixing strategy can be successfully and practicably approximated by the mix-norm minimisation since we find that the mix-norm-optimal initial perturbations are far less sensitive to changes in the target time horizon than their optimal variance-minimising counterparts.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.388
      Issue No: Vol. 850 (2018)
  • Developed liquid film passing a trailing edge under the action of gravity
           and capillarity
    • Authors: B. Scheichl; R. I. Bowles, G. Pasias
      Pages: 924 - 953
      Abstract: We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.464
      Issue No: Vol. 850 (2018)
  • Role of Klebanoff modes in active flow control of separation: direct
           numerical simulations
    • Authors: Shirzad Hosseinverdi; Hermann F. Fasel
      Pages: 954 - 983
      Abstract: Our previous research has shown that an active flow control strategy using two-dimensional (2-D) harmonic blowing and suction with properly chosen frequency and amplitude can significantly reduce the separation region, delay transition to turbulence and can even relaminarize the flow. How such effective flow control for transition delay and relaminarization is affected by free-stream turbulence (FST) remains an open question. In order to answer this question, highly resolved direct numerical simulations (DNS) are carried out where very low-amplitude isotropic FST fluctuations are introduced at the inflow boundary of the computational domain. With FST the effectiveness of the flow control is not diminished, and the extent of the separated flow region is reduced by the same amount as for the zero FST case. However, a striking difference observed in the DNS is the fact that in the presence of even very low levels of FST, the flow transitions shortly downstream of the reattachment location of the bubble, contrary to the case without FST. It appears that this different behaviour for even very small levels of FST is caused by an interaction between the high-amplitude 2-D disturbances introduced by the flow control forcing and 3-D Klebanoff modes (K-modes) that are generated by the FST. The streamwise elongated streaks due to the K-modes cause a spanwise-periodic modulation of the basic flow and subsequently of the primary 2-D wave. The disturbances associated with this modulation exhibit strong growth and initiate the breakdown process to turbulence. Linear secondary instability investigations with respect to low-frequency 3-D disturbances are carried out based on the linearized Navier–Stokes equations. The response of the forced flow to the low-frequency 3-D disturbances reveals that the time-periodic base flow is unstable with respect to a wide range of 3-D modes. In particular, the wavelength associated with the spanwise spacing of the K-mode falls into the range of, and is in fact very close to, the most unstable 3-D disturbances. Results from the secondary instability analysis and the comparison with DNS results, support the conjecture that the forcing amplitude has a major impact on the onset and amplification rate of the K-modes: lowering the forcing amplitude postpones the onset of the growth of the K-modes and reduces the growth rate of the K-modes for a given FST intensity. The net effect of these two events is a delay of the transition onset. Nevertheless, the instability mechanism that governs the transition process is the same as previously identified, i.e. interaction of the K-mode and 2-D primary wave. Furthermore, for low levels of FST, the amplitude of the low-frequency K-modes scales linearly with the FST intensity in the approach boundary layer up to the secondary instability regime.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.489
      Issue No: Vol. 850 (2018)
  • Confined inclined thermal convection in low-Prandtl-number fluids
    • Authors: Lukas Zwirner; Olga Shishkina
      Pages: 984 - 1008
      Abstract: Any tilt of a Rayleigh–Bénard convection cell against gravity changes the global flow structure inside the cell, which leads to a change of the heat and momentum transport. Especially sensitive to the inclination angle is the heat transport in low-Prandtl-number fluids and confined geometries. The purpose of the present work is to investigate the global flow structure and its influence on the global heat transport in inclined convection in a cylindrical container of diameter-to-height aspect ratio $\unicode[STIX]{x1D6E4}=1/5$ . The study is based on direct numerical simulations where two different Prandtl numbers $Pr=0.1$ and 1.0 are considered, while the Rayleigh number, $Ra$ , ranges from $10^{6}$ to $10^{9}$ . For each combination of $Ra$ and $Pr$ , the inclination angle is varied between 0 and $\unicode[STIX]{x03C0}/2$ . An optimal inclination angle of the convection cell, which provides the maximal global heat transport, is determined. For inclined convection we observe the formation of two system-sized plume columns, a hot and a cold one, that impinge on the opposite boundary layers. These are related to a strong increase in the heat transport.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.477
      Issue No: Vol. 850 (2018)
  • Progression of heavy plates from stable falling to tumbling flight
    • Authors: Edwin M. Lau; Wei-Xi Huang, Chun-Xiao Xu
      Pages: 1009 - 1031
      Abstract: This study examines the transition of stable falling to tumbling flight for freely falling heavy plates in a two-dimensional viscous fluid, solved via direct numerical simulation with the immersed boundary method. The simulations are performed at a range of Reynolds number ( $Re$ ) of up to 500 and a dimensionless moment of inertia ( $I^{\ast }$ ) up to 10. It is found that a plate may settle to stable falling or develop into tumbling descent depending on the initial angle of release $\unicode[STIX]{x1D703}_{0}$ . The characteristics and performance that distinguish two flight states are investigated. This bistability is analysed with phase portraits and the region mapped across the regime of $I^{\ast }$ and $Re$ at a specific thickness ratio. In determining the flight state, the respective critical $\unicode[STIX]{x1D703}_{0}$ is found to follow a power law through $I^{\ast }$ and $Re$ . It is suggested that the changing slope of the lift curve that the plate undergoes sets the two flight states apart. Flow fields also reveal that the recirculation behind the plate is confined by the vortex structures and provides an additional rotation to the plate. An experiment is performed suggesting that bistability also occurs at Re ${\sim}O(10^{4})$ . Other shapes are also simulated and the different bistable effects are discussed.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.486
      Issue No: Vol. 850 (2018)
  • Source and boundary condition effects on unconfined and confined
           vertically distributed turbulent plumes
    • Authors: N. B. Kaye; P. Cooper
      Pages: 1032 - 1065
      Abstract: Plumes generated by vertically distributed sources of buoyancy have been observed to have substantially lower entrainment coefficients than their equivalent-geometry constant buoyancy flux plumes. Two differences between distributed and localized sources of buoyancy are the presence of a wall shear stress at the source and that non-ideal source conditions are distributed over the whole height of the enclosure for a vertically distributed source. Herein the impact of non-ideal source and boundary conditions on vertically distributed plumes is analysed. It is shown that, at small heights, the plume volume flow rate is significantly influenced by the wall-source volume flux. At larger heights the wall-source buoyancy is greater than the mean plume buoyancy, creating a non-self-similar horizontal buoyancy distribution within the plume. Recent experiments into the behaviour of a vertically distributed source of buoyancy in a confined region have also shown that the plume partially detrains in the stratified region of the enclosure. This detrainment has not been observed for constant buoyancy flux plumes in a confined region. Although models have been proposed to quantify the detrainment process, it is still unclear why vertically distributed buoyancy sources detrain while constant buoyancy flux plumes do not in the same physical geometry. The impact of source and boundary effects on previously published experiments on vertically distributed plumes are reviewed and the possible implications for plume entrainment and detrainment are discussed.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.487
      Issue No: Vol. 850 (2018)
  • Flat plate impact on water
    • Authors: Hans C. Mayer; Rouslan Krechetnikov
      Pages: 1066 - 1116
      Abstract: While the classical problem of a flat plate impact on a water surface at zero dead-rise angle has been studied for a long time both theoretically and experimentally, it still presents a number of challenges and unsolved questions. Hitherto, the details of the flow field – especially at early times and close to the plate edge, where the classical inviscid theory predicts a singularity in the velocity field and thus in the free surface deflection, so-called ejecta – have not been studied experimentally, which led to mutually contradicting suppositions in the literature. On one hand, it motivated Yakimov’s self-similar scaling near the plate edge. On the other hand, a removal of the singularity was previously suggested with the help of the Kutta–Joukowsky condition at the plate edge, i.e. enforcing the free surface to depart tangentially to the plate. In the present experimental study we were able to overcome challenges with optical access and investigate, for moderate Reynolds ( $0.5
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.461
      Issue No: Vol. 850 (2018)
  • On the transient response of the turbulent boundary layer inception in
           compressible flows
    • Authors: J. Saavedra; G. Paniagua, S. Lavagnoli
      Pages: 1117 - 1141
      Abstract: The behavioural characteristics of thermal boundary layer inception dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the thermal boundary layer to be established is vital to optimize flow control strategies, as well as the thermal management of systems exposed to ephemeral phenomena, typically on the millisecond scale. This paper presents the time characterization of the momentum and thermal boundary layer development in transient turbulent compressible air flows. We present a new framework to perform such estimations based on detailed unsteady Reynolds averaged Navier–Stokes simulations that may be extended to higher fidelity simulations. First of all, the aerodynamic boundary layer initiation is described using adiabatic simulations. Additional numerical calculations were then performed by setting the isothermal wall condition to evaluate the additional time required by the thermal boundary layer to establish after the aerodynamic boundary layer reaches its steady state. Finally, full conjugate simulations were executed to compute the warm up effect of the solid during the blowdown of a hot fluid over a colder metallic test model. The transient performance of the turbulent thermal and momentum boundary layers is quantified through numerical simulations of air blowdown over a flat plate for different mainstream flow conditions. The effects of Reynolds number, free stream velocity, transient duration, test article length and free stream temperature were independently assessed, to then define a mathematical expression of the momentum boundary layer settlement. This paper presents a novel numerical correlation of the additional time required by the thermal boundary layer to be stablished after the settlement of the momentum boundary layer. The time scales of the aerodynamic and thermal boundary layers are presented as a function of relevant non-dimensional numbers, as well as the description of the response of the near wall flow to sudden free stream changes. The characterization of the boundary layer mechanisms discussed in this paper contribute to the establishment of an evidence-based foundation for advances in the field of flow control.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.502
      Issue No: Vol. 850 (2018)
  • Effect of transverse temperature gradient on the migration of a deformable
           droplet in a Poiseuille flow
    • Authors: Sayan Das; Shubhadeep Mandal, Suman Chakraborty
      Pages: 1142 - 1171
      Abstract: Intricate manipulation of droplets in fluidic confinements may turn out to be critically important for achieving their controlled transverse distributions. Here, we study the migration characteristics of a suspended deformable droplet in a parallel plate channel under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. An outstanding question concerning the resultant non-trivial dynamical features that we address here pertains to the nonlinearity that results as a consequence of the shape deformation, which does not permit us to analyse the combined transport as a mere linear superposition of the results for the thermocapillary and imposed flow driven droplet migration in an effort to obtain the final solution. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia or thermal convection of the fluid in either of the phases. To obtain a numerical solution, we use the conservative level set method. We perform numerical simulations over a wide range of governing parameters and obtain the dependence of the transverse steady position of the droplet on different parameters. In order to address practical microfluidic set-ups, the influence of a bounding wall as well as the effect of thermal convection and finite shape deformation on the cross-stream migration of the droplet is investigated through numerical simulations. Increase in the thermal Marangoni stress shifts the steady-state transverse position of the droplet further away from the channel centreline, for any particular value of the capillary number (which signifies the ratio of the viscous force to the surface tension force). The confinement ratio, which is the ratio of the droplet radius to the channel height, plays an important role in predicting the transverse position of the droplet and thus has immense consequences for the design of droplet-based microfluidic devices with enhanced functionalities. A large confinement ratio drives the droplet towards the channel centre, whereas a smaller confinement ratio causes the droplet to move towards the wall. Moreover, for a fixed droplet radius and constant imposed temperature gradient, an increase in the channel height results in an increase in the time required for the droplet to reach the steady-state position. However, the final steady-state position of the droplet is independent of its initial position but at the same time dependent on the droplet phase thermal conductivity. A larger droplet thermal conductivity compared with the carrier phase results in a steady-state droplet position closer to the channel centreline. A higher fluid inertia, on the other hand, shifts the steady-state position towards the channel wall.
      PubDate: 2018-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2018.493
      Issue No: Vol. 850 (2018)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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