相关论文: The Oberbeck--Boussinesq Approximation as a Consti…
We consider a general compressible viscous and heat conducting fluid confined between two parallel plates and heated from the bottom. The time evolution of the fluid is described by the Navier--Stokes--Fourier system considered in the…
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 uids with positive heat conductivity and zero conductivity…
By using a formulation of a class of compressible viscous flows with a heat source via vorticity and expansion-rate, we study the Oberbeck-Boussinesq flows. To this end we establish a new integral representation for solutions of parabolic…
The Oberbeck-Boussinesq approximation is the most widely employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the…
We consider a general compressible, viscous, heat and magnetically conducting fluid described by the compressible Navier-Stokes-Fourier system coupled with induction equation. In particular, we do not assume conservative boundary conditions…
We consider the Oberbeck--Boussinesq approximation driven by an inhomogeneous temperature distribution on the boundary of a bounded fluid domain. The relevant boundary conditions are perturbed by a non--local term arising in the…
The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…
Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variation. In this paper the linear analysis of the…
In contrast with a large variety of conventional models of thermally driven fluids, we show that the standard Oberbeck--Boussinesq approximation \emph{cannot} be obtained as a singular limit of the Navier--Stokes--Fourier system in the…
A thermodynamic argument is proposed in order to discuss the most appropriate form of the local energy balance equation within the Oberbeck-Boussinesq approximation. The study is devoted to establish the correct thermodynamic property to be…
We determine the asymptotic conditions under which the Boussinesq approximation is valid for oscillatory convection in a rapidly rotating fluid. In the astrophysically relevant parameter regime of small Prandtl number, we show that the…
This paper shows that the energetics of Boussinesq and anelastic fluids possesses a term that can be identified as the approximation $\delta W_{ba}$ to the compressible work of expansion/contraction $\delta W =-P {\rm d}\upsilon$, where $P$…
The equations of motion describing buoyant fluids are often simplified using a set of approximations proposed by J. Boussinesq one century ago. To resume, they consist in assuming constant fluid properties, incompressibility and…
The \emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related…
In an Oberbeck-Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for the B\'enard problem occurs at a higher critical Rayleigh number. Since of the difficulties related to…
In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic…
We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier problem. As one possible singular limit may be obtained the…
We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero…
We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell…
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical direction. For initial conditions satisfying a…