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Journal of Fluid Mechanics
Journal Prestige (SJR): 1.591
Citation Impact (citeScore): 3
Number of Followers: 197  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0022-1120 - ISSN (Online) 1469-7645
Published by Cambridge University Press Homepage  [387 journals]
  • Instability of a thin viscous film flowing under an inclined substrate:
           steady patterns
    • Authors: Gaétan Lerisson; Pier Giuseppe Ledda, Gioele Balestra, François Gallaire
      Abstract: The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a stationary localized perturbation, a front develops that we predict with the group velocity of the unstable wave packet. We compare our experimental measurements with numerical solutions of the nonlinear lubrication equation with complete curvature. Streamwise structures dominate and saturate after some distance. We recover their profile with a one-dimensional lubrication equation suitably modified to ensure an invariant profile along the streamwise direction and compare them with the solution of a purely two-dimensional pendent drop, showing overall a very good agreement. Finally, those different profiles agree also with a two-dimensional simulation of the Stokes equations.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.396
      Issue No: Vol. 898 (2020)
  • Reference map technique for incompressible fluid–structure
    • Authors: Chris H. Rycroft; Chen-Hung Wu, Yue Yu, Ken Kamrin
      Abstract: We present a general simulation approach for fluid–solid interactions based on the fully Eulerian reference map technique. The approach permits the modelling of one or more finitely deformable continuum solid bodies interacting with a fluid and with each other. A key advantage of this approach is its ease of use, as the solid and fluid are discretized on the same fixed grid, which greatly simplifies the coupling between the phases. We use the method to study a number of illustrative examples involving an incompressible Navier–Stokes fluid interacting with multiple neo-Hookean solids. Our method has several useful features including the ability to model solids with sharp corners and the ability to model actuated solids. The latter permits the simulation of active media such as swimmers, which we demonstrate. The method is validated favourably in the flag-flapping geometry, for which a number of experimental, numerical and analytical studies have been performed. We extend the flapping analysis beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.353
      Issue No: Vol. 898 (2020)
  • Phase separation effects on a partially miscible viscous fingering
    • Authors: Ryuta X. Suzuki; Yuichiro Nagatsu, Manoranjan Mishra, Takahiko Ban
      Abstract: Classical viscous fingering (VF) instability, the formation of finger-like interfacial patterns, occurs when a less viscous fluid displaces a more viscous one in porous media in immiscible and fully miscible systems. However, the dynamics in partially miscible fluid pairs, exhibiting a phase separation due to its finite solubility into each other, has not been largely understood so far. This study has succeeded in experimentally changing the solution system from immiscible to fully miscible or partially miscible by varying the compositions of the components in an aqueous two-phase system (ATPS) while leaving the viscosities relatively unchanged at room temperature and atmospheric pressure. Here, we have experimentally discovered a new topological transition of VF instability by performing a Hele-Shaw cell experiment using the partially miscible system. The finger formation in the investigated partially miscible system changes to the generation of spontaneously moving multiple droplets. Through additional experimental investigations, we determine that such anomalous VF dynamics is driven by thermodynamic instability such as phase separation due to spinodal decomposition and Korteweg convection induced by compositional gradient during such phase separation. We perform the numerical simulation by coupling hydrodynamics with such chemical thermodynamics and the spontaneously moving droplet dynamics is obtained, which is in good agreement with the experimental investigations of the ATPS. This numerical result strongly supports our claim that the origin of such anomalous VF dynamics is thermodynamic instability.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.406
      Issue No: Vol. 898 (2020)
  • Fragmentation versus Cohesion
    • Authors: Emmanuel Villermaux
      Abstract: Capillarity is the familiar manifestation of the cohesion of liquids. Since Laplace (Traité de mécanique céleste, vol. IV, supplément au livre X: Sur l’action capillaire, 1805, pp. 1–65), we know that intense attractive forces between the molecules bridge the small with the large as they shape liquid/vapour interfaces at the macroscopic scale through the concept of surface tension (menisci, drops, bubbles, puddles, liquid rise in tubes, etc. …). We concentrate on situations where liquids ‘disgregate’, following the neologism of Clausius (Phil. Mag., vol. 24 (159), 1862, pp. 81–97), meaning that they fragment by the action of deformation stresses whose intensity competes with that of cohesion forces. Various examples, including explosions, blow-ups, hard and soft impacts and shears applied to liquid jets, sheets and drops are reviewed. They concern applications ranging from liquid propulsion, agricultural spraying, to the formation of ocean spray, raindrops and human exhalations by violent respiratory events. In spite of their diversity, the various modes of fragment production share an ultimate common phenomenology – the ligament dynamics – suggesting that the final stable droplet size distribution can be interpreted from elementary principles.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.366
      Issue No: Vol. 898 (2020)
  • Structure function tensor equations in inhomogeneous turbulence
    • Authors: Davide Gatti; Alessandro Chiarini, Andrea Cimarelli, Maurizio Quadrio
      Abstract: Exact budget equations for the second-order structure function tensor $\langle \unicode[STIX]{x1D6FF}u_{i}\unicode[STIX]{x1D6FF}u_{j}\rangle$ , where $\unicode[STIX]{x1D6FF}u_{i}$ is the difference of the $i$ th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of $\langle \unicode[STIX]{x1D6FF}u_{i}\unicode[STIX]{x1D6FF}u_{j}\rangle$ . The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=200$ is considered. The off-diagonal component $\langle -\unicode[STIX]{x1D6FF}u\unicode[STIX]{x1D6FF}v\rangle$ , which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at $Re_{\unicode[STIX]{x1D70F}}=500$ and $1000$ . In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.399
      Issue No: Vol. 898 (2020)
  • Mixing in forced stratified turbulence and its dependence on large-scale
    • Authors: Christopher J. Howland; John R. Taylor, C. P. Caulfield
      Abstract: We study direct numerical simulations of turbulence arising from the interaction of an initial background shear, a linear background stratification and an external body force. In each simulation the turbulence produced is spatially intermittent, with dissipation rates varying over orders of magnitude in the vertical. We focus analysis on the statistically quasi-steady states achieved by applying large-scale body forcing to the domain, and compare flows forced by internal gravity waves with those forced by vertically uniform vortical modes. By considering the turbulent energy budgets for each simulation, we find that the injection of potential energy from the wave forcing permits a reversal in the sign of the mean buoyancy flux. This change in the sign of the buoyancy flux is associated with large, convective density overturnings, which in turn lead to more efficient mixing in the wave-forced simulations. The inhomogeneous dissipation in each simulation allows us to investigate localised correlations between the kinetic and potential energy dissipation rates. These correlations lead us to the conclusion that an appropriate definition of an instantaneous mixing efficiency, $\unicode[STIX]{x1D702}(t):=\unicode[STIX]{x1D712}/(\unicode[STIX]{x1D712}+\unicode[STIX]{x1D700})$ (where $\unicode[STIX]{x1D700}$ and $\unicode[STIX]{x1D712}$ are the volume-averaged turbulent viscous dissipation rate and fluctuation density variance destruction rate respectively) in the wave-forced cases is independent of an appropriately defined local turbulent Froude number, consistent with scalings proposed for low Froude number stratified turbulence.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.383
      Issue No: Vol. 898 (2020)
  • Single-time Markovianized spectral closure in fluid turbulence
    • Authors: Takuya Kitamura
      Abstract: Kaneda’s (J. Fluid Mech., vol. 107, 1981, pp. 131–145) Lagrangian renormalized approximation was extended to single-time spectral closure under two assumptions: (i) Markovianization and (ii) the Lagrangian velocity response function is expressed by $G(k,\unicode[STIX]{x1D70F})=\exp (-C_{1}(k)\unicode[STIX]{x1D70F}-C_{2}(k)\unicode[STIX]{x1D70F}^{2}/2)$ . The unknown functions $C_{1}(k)$ and $C_{2}(k)$ are theoretically derived to be consistent with the exact short-time behaviour of $G(k,\unicode[STIX]{x1D70F})$ and the asymptotic short-time behaviour of assumed exponential form of $G(k,\unicode[STIX]{x1D70F})$ , i.e. the present closure is derived from the Navier–Stokes equation without introduction of any adjustable parameters and it can calculate the statistical quantities by theory. The results show that the present closure has good agreement with direct numerical simulation for single- and two-point statistics.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.415
      Issue No: Vol. 898 (2020)
  • Acoustic propulsion of a small, bottom-heavy sphere
    • Authors: François Nadal; Sébastien Michelin
      Abstract: We present here a comprehensive derivation for the speed of a small bottom-heavy sphere forced by a transverse acoustic field and thereby establish how density inhomogeneities may play a critical role in acoustic propulsion. The sphere is trapped at the pressure node of a standing wave whose wavelength is much larger than the sphere diameter. Due to its inhomogeneous density, the sphere oscillates in translation and rotation relative to the surrounding fluid. The perturbative flows induced by the sphere’s rotation and translation are shown to generate a rectified inertial flow responsible for a net mean force on the sphere that is able to propel the particle within the zero-pressure plane. To avoid an explicit derivation of the streaming flow, the propulsion speed is computed exactly using a suitable version of the Lorentz reciprocal theorem. The propulsion speed is shown to scale as the inverse of the viscosity, the cube of the amplitude of the acoustic field and is a non-trivial function of the acoustic frequency. Interestingly, for some combinations of the constitutive parameters (fluid-to-solid density ratio, moment of inertia and centroid to centre of mass distance), the direction of propulsion is reversed as soon as the frequency of the forcing acoustic field becomes larger than a certain threshold. The results produced by the model are compatible with both the observed phenomenology and the orders of magnitude of the measured velocities.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.401
      Issue No: Vol. 898 (2020)
  • Tenacious wall states in thermal convection in rapidly rotating containers
    • Authors: Olga Shishkina
      Abstract: Convection in a container, heated from below, cooled from above and rapidly rotated around a vertical axis, starts from its sidewall. When the imposed vertical temperature gradient is not sufficiently large for bulk modes to set in, thermal convection can start in the form of wall modes, which are observed near the sidewall as pairs of hot ascending and cold descending plumes that drift along the wall. With increasing temperature gradient, different wall and bulk modes occur and interact, leading finally to turbulence. A recent numerical study by Favier & Knobloch (J. Fluid Mech., 895, 2020, R1) reveals an extreme robustness of the wall states. They persist above the onset of bulk modes and turbulence, thereby relating them to the recently discovered boundary zonal flows in highly turbulent rotating thermal convection. More exciting is that the wall modes can be thought of as topologically protected states, as they are robust with respect to the sidewall shape. They stubbornly drift along the wall, following its contour, independent of geometric obstacles.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.420
      Issue No: Vol. 898 (2020)
  • Reduced-order modelling of thick inertial flows around rotating cylinders
    • Authors: Alexander W. Wray; Radu Cimpeanu
      Abstract: A new model for the behaviour of a thick, two-dimensional layer of fluid on the surface of a rotating cylinder is presented, incorporating the effects of inertia, rotation, viscosity, gravity and capillarity. Comparisons against direct numerical simulations (DNS) show good accuracy for fluid layers of thickness of the same order as the cylinder radius, even for Reynolds numbers up to $Re\sim 10$ . A rich and complex parameter space is revealed, and is elucidated via a variety of analytical and numerical techniques. At moderate rotation rates and fluid masses, the system exhibits either periodic behaviour or converges to a steady state, with the latter generally being favoured by greater masses and lower rotation rates. These behaviours, and the bifurcation structure of the transitions between them, are examined using a combination of both the low-order model and DNS. Specific attention is dedicated to newly accessible regions of parameter space, including the multiple steady state solutions observed for the same parameter values by Lopes et al. (J. Fluid Mech., vol. 835, 2018, pp. 540–574), where the corresponding triple limit point bifurcation structure is recovered by the new low-order model. We also inspect states in which the interface becomes multivalued – and thus outside the reach of the reduced-order model – via DNS. This leads to highly nonlinear multivalued periodic structures appearing at moderate thicknesses and relatively large rotation rates. Even much thicker films may eventually reach steady states (following complex early evolution), provided these are maintained by a combination of forces sufficiently large to counteract gravity.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.421
      Issue No: Vol. 898 (2020)
  • Reduced-order modelling of radiative transfer effects on
           Rayleigh–Bénard convection in a cubic cell
    • Authors: Laurent Soucasse; Bérengère Podvin, Philippe Rivière, Anouar Soufiani
      Abstract: This paper presents a reduced-order modelling strategy for Rayleigh–Bénard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh–Bénard cell is performed for an $\text{air}/\text{H}_{2}\text{O}/\text{CO}_{2}$ mixture at room temperature and at a Rayleigh number of $10^{7}$ . It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of $\unicode[STIX]{x03C0}/2$ of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an a priori model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.395
      Issue No: Vol. 898 (2020)
  • Connecting the time evolution of the turbulence interface to coherent
    • Authors: Marius M. Neamtu-Halic; Dominik Krug, Jean-Paul Mollicone, Maarten van Reeuwijk, George Haller, Markus Holzner
      Abstract: The surface area of turbulent/non-turbulent interfaces (TNTIs) is continuously produced and destroyed via stretching and curvature/propagation effects. Here, the mechanisms responsible for TNTI area growth and destruction are investigated in a turbulent flow with and without stable stratification through the time evolution equation of the TNTI area. We show that both terms have broad distributions and may locally contribute to either production or destruction. On average, however, the area growth is driven by stretching, which is approximately balanced by destruction by the curvature/propagation term. To investigate the contribution of different length scales to these processes, we apply spatial filtering to the data. In doing so, we find that the averages of the stretching and the curvature/propagation terms balance out across spatial scales of TNTI wrinkles and this scale-by-scale balance is consistent with an observed scale invariance of the nearby coherent vortices. Through a conditional analysis, we demonstrate that the TNTI area production (destruction) is localized at the front (lee) edge of the vortical structures in the interface proximity. Finally, we show that while basic mechanisms remain the same, increasing stratification reduces the rates at which TNTI surface area is produced as well as destroyed. We provide evidence that this reduction is largely connected to a change in the multiscale geometry of the interface, which tends to flatten in the wall-normal direction at all active length scales of the TNTI.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.414
      Issue No: Vol. 898 (2020)
  • Péclet-number dependence of small-scale anisotropy of passive scalar
           fluctuations under a uniform mean gradient in isotropic turbulence
    • Authors: Tatsuya Yasuda; Toshiyuki Gotoh, Takeshi Watanabe, Izumi Saito
      Abstract: We study passive scalar fluctuations convected by statistically stationary homogeneous isotropic turbulence under a uniform mean scalar gradient. In order to elucidate the parameter dependence of small-scale statistics of scalar fluctuations, we conduct direct numerical simulations of passive scalar turbulence with 59 different combinations of Reynolds number and Schmidt number. For all the cases, we compute time-average statistics of various quantities, which include the scalar derivative skewness and flatness, the ratio of parallel-to-perpendicular scalar-gradient variances, and the anisotropy parameter recently proposed (Hill, Phys. Rev. Fluids, vol. 2, 2017, 094601). Notably, the degree of small-scale anisotropy of passive scalar fluctuation is characterised by a universal function of the Péclet number $Pe_{\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}}=u^{\prime }\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}/\unicode[STIX]{x1D705}$ , where $u^{\prime }$ is the root mean square velocity, $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$ the Taylor microscale of scalar fluctuation, $\unicode[STIX]{x1D705}$ the mass diffusivity. In the definition of the Péclet number, the use of $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$ , rather than the Taylor microscale of velocity fluctuation, is key to collapsing the data of different Reynolds and Schmidt numbers. When the Péclet number is low, large-scale anisotropic scalar structures emerge irrespective of the Reynolds number. These structures are elongated along the direction of the uniform mean scalar gradient, and their size is significantly larger than the integral length scale of velocity fluctuation.
      PubDate: 2020-09-10T00:00:00.000Z
      DOI: 10.1017/jfm.2020.419
      Issue No: Vol. 898 (2020)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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