相关论文: Internal heating driven convection at infinite Pra…
A series of numerical simulations of Rayleigh-B{\'e}nard convection in a cubic cavity are conducted in order to examine the structure of the thermal boundary layer in case of mixed boundary conditions. The main goal of the study is the…
A Rayleigh-B\'enard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range $0.7<Pr<21$ and for the full range of soft and hard turbulences, up to Rayleigh number $Ra\simeq 10^{11}$. The…
A numerical method is presented which conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with…
The Rayleigh number $Ra$ dependence of the Nusselt number $Nu$ in turbulent Rayleigh--B\'enard convection is numerically investigated for a moderate and low Prandtl number, $Pr=0.7$ and $0.021$, respectively. Here we specifically address…
We study the dynamical regimes of a density-stratified fluid confined between isothermal no-slip top and bottom boundaries (at temperatures $T_t$ and $T_b$) via direct numerical simulation. The thermal expansion coefficient of the fluid is…
We consider two hydrodynamic model problems (one incompressible and one compressible) with three dimensional fluid flow on the torus and temperature-dependent viscosity and conductivity. The ambient heat for the fluid is transported by the…
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a…
Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with…
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on…
Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single…
The threshold conditions to convective instability in a semi-infinite porous layer saturated by a fluid are determined. The classical setup for this problem in geothermal fluid dynamics was originally modelled by Wooding in 1960. Its…
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive…
We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for the Dirichlet…
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…
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
Rayleigh-B\'enard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of…
Numerical simulations for 2-D unsteady, incompressible flow with heat transfer in a four-sided lid-driven rectangular domain are reported in the present study. For the four-sided lid-driven rectangular domain, the lower wall is moved to the…
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 consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…