Stéphane Zaleski

Scaling of hard thermal turbulence in Rayleigh-Bénard convection

An experimental study of Rayleigh-Benard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 10 7 Ra 12 ) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra . However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu , proportional to

Lattice-gas cellular automata : simple models of complex hydrodynamics

Ra^{\frac{1}{3}}

Droplet Splashing on a Thin Liquid Film

while experiment gives an index much closer to

Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces

\frac{2}{7}

Two-dimensional Navier–Stokes simulation of breaking waves

. A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

Bubble collapse near a solid boundary: a numerical study of the influence of viscosity

Preface Acknowledgements 1. A simple model of fluid mechanics 2. Two routes to hydrodynamics 3. Inviscid two-dimensional lattice-gas hydrodynamics 4. Viscous two-dimensional hydrodynamics 5. Some simple 3D models 6. The lattice-Boltzmann method 7. Using the Boltzmann method 8. Miscible fluids 9. Immiscible lattice gases 10. Lattice-Boltzmann method for immiscible fluids 11. Immiscible lattice gases in three dimensions 12. Liquid-gas models 13. Flow through porous media 14. Equilibrium statistical mechanics 15. Hydrodynamics in the Boltzmann approximation 16. Phase separation 17. Interfaces 18. Complex fluids and patterns Appendices Author Index Subject Index.

A mesh-dependent model for applying dynamic contact angles to VOF simulations

We propose a theory predicting the transition between splashing and deposition for impacting drops. This theory agrees with current experimental observations and is supported by numerical simulations. It assumes that the width of the ejected liquid sheet during impact is precisely controlled by a viscous length l ν . Numerous predictions follow this theory and they compare well with recent experiments reported by Thoroddsen [J. Fluid Mech. 451, 373 (2002)].

Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry

Abstract We present a large number of new geometric, ergodic and statistical properties of the Kuramoto-Sivashinsky equation modeling interfacial turbulence in various physical contexts. In addition, this equation has the remarkable property of inertial manifolds where some finite-dimensional dynamical system is rigorously equivalent to this infinite-dimensional partial differential equation. In moderate size domains (up to ten periods in length) a low-dimensional vector field skeleton underpins even strongly chaotic regimes and controls the bifurcations of the inertial manifold. The extreme numerical sensitivity of chaos in this dissipative PDE requires very high precision methods. Despite the geometrical complexities of the bifurcation structure, some statistical properties remain remarkably simple. There is overwhelming evidence that for some parameter values a permanent unsteady state exists. An unexpectedly simple diffusive relaxation of the large-scale fluctuations is extracted from extensive numerical simulations. In these calculations we observe long time tails for the correlation functions of relevant quantities. We propose an explanation in terms of an effective viscosity and compare the transport in the weakly turbulent interface with related theories for random interfaces and developed turbulence.

Drop dynamics after impact on a solid wall: Theory and simulations

Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.

Numerical simulation of droplets, bubbles and waves : state of the art

The effect of viscosity on jet formation for bubbles collapsing near solid boundaries is studied numerically. A numerical technique is presented which allows the Navier-Stokes equations with free-surface boundary conditions to be solved accurately and efficiently. Good agreement is obtained between experimental data and numerical simulations for the collapse of large bubbles. However, it is shown that compressible and thermal effects must be taken into account in order to describe the energy dissipation occurring during jet impact correctly. A parametric study of the effect of viscosity on jet impact velocity is undertaken. The jet impact velocity is found to decrease as viscosity increases and above a certain threshold jet impact is impossible. We study how this critical Reynolds number depends on the initial radius and the initial distance from the wall. A simple scaling law is found to link this critical Reynolds number to the other non-dimensional parameters of the problem.