Lattice Boltzmann equations for the isothermal Navier-Stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory. Applied to the shallow water equations, with its different equation of state, the same approach yields discrete equilibria that are subject to a grid scale computational instability....

We propose a hydrodynamic mechanism, based on the Marangoni flow, to describe growth instabilities of liquid-condensed islands in the supercooled liquid-expanded phase of two-dimensional Langmuir monolayers. This Marangoni instability is intrinsic to Langmuir monolayers and is not controlled by the expulsion of chemical impurities from the liquid-condensed phase. The hydrodynamic transport of t...

The three-dimensional instability of the thermocapillary convection in cylindrical undeformable floating zones heated laterally is studied numerically. Different types of the boundary conditions, including radiation heating, linearized radiation and prescribed heat flux are used in the calculation. Stability diagrams showing the Prandtl number dependence of the critical Marangoni numbers that r...

■ Abstract The Richtmyer-Meshkov instability arises when a shock wave interacts with an interface separating two different fluids. It combines compressible phenomena, such as shock interaction and refraction, with hydrodynamic instability, including nonlinear growth and subsequent transition to turbulence, across a wide range of Mach numbers. This review focuses on the basic physical processes ...