Thermal instability of nonhomogeneous fluids

Global Instability in Strongly Nonhomogeneous Systems

Error estimates for semi-Galerkin approximations of nonhomogeneous incompressible fluids

We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the H norm for the velocity. We also derive an error estimate for the density ...

Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids

We consider spectral semi-Galerkin approximations for the strong solutions of the nonhomogeneous Navier-Stokes equations. We derive an optimal uniform in time error bound in the H 1 norm for approximations of the velocity. We also derive an error estimate for approximations of the density in some spaces L r .

Faraday’s Instability for Viscous Fluids

We derive an exact equation which is nonlocal in time for the linear evolution of the surface of a viscous fluid, and show that this equation becomes local and of second order in an interesting limit. We use our local equation to study Faraday’s instability in a strongly dissipative regime and find a new scenario which is the analog of the Rayleigh-Taylor instability. Analytic and numerical cal...

Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability

Starting from the linearized fluctuating Boussinesq equations we derive an expression for the structure factor of fluids in stationary convection-free thermal nonequilibrium states, taking into account both gravity and finite-size effects. It is demonstrated how the combined effects of gravity and finite size causes the structure factor to go through a maximum value as a function of the wave nu...