In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of fluids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity f...

In this paper we study finite dimensional approximations to Boussinesq type equations. Our methods are based on infinite dimensional center manifold theory. The main advantage of our approach is that we can handle both well-posed and ill-posed versions of the Boussinesq equation. We show that for suitable initial conditions, our approximations describe the dynamics accurately for long enough ti...

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluid...

Measurements of the Nusselt number N as a function of the Rayleigh number R using ethane gas near its critical point show that N is enhanced by non-Oberbeck-Boussinesq (NOB) effects when the top temperature approaches the coexistence curve. The empirical criterion that a small ∆ρ/ρ (ρ is the density) implies Boussinesq behavior is found not to be valid. An examination of data by Chavanne et al....

We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Fin...

In this paper we review and clarify some aspects of the asymptotic analysis of the compressible Navier Stokes equations in the low Mach number limit. In the absence of heat exchange (the isentropic regime) this limit is well understood and rigorous results are available. When heat exchange is considered different simplified models can be obtained, the most famous being the Boussinesq approximat...

This paper is concerned with the local well-posedness of Oberbeck Boussinesq approximation for unsteady motion a drop in another fluid separated by closed interface surface tension. We are devoted to obtaining linearized Oberbeck-Boussinesq fixed domain using Hanzawa transformation, and maximal $ L^{p} $-$ L^{q} regularities two-phase system obtained authors [10] establish existence uniqueness ...

A class of model equations that describe the bi-directional propagation of small amplitude long waves on the surface of shallow water is derived from two-dimensional potential flow equations at various orders of approximation in two small parameters, namely the amplitude parameter a 1⁄4 a=h0 and wavelength parameter b 1⁄4 ðh0=lÞ2, where a and l are the actual amplitude and wavelength of the sur...

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a BénardMarangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussines...

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification int...