Related papers: Applicability of Boussinesq approximation in a tur…
We investigate the nonlinear stability problem for the two-dimensional Boussinesq system around the Poiseuille flow in a finite channel. The system has the characteristic of Navier-slip boundary condition for the velocity and Dirichlet…
Penetrative turbulent Rayleigh-B\'enard convection which depends on the density maximum of water near $4^\circ\rm{C}$ is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is…
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…
A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression…
Rayleigh-B\'enard convection is numerically simulated in two- and three-dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the…
To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a…
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…
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…
Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on…
Recently, Kaladze and Misra [Phys. Scr. 99 (2024) 085013] showed that the tropospheric stratified fluid flows may be unstable by the effects of the negative temperature gradient and the temperature-dependent density inhomogeneity arising…
Fully resolved simulations are used to quantify the effects of heat transfer in the presence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ($Re$) in the range $10^{-3} \le Re \le 10$ in a…
This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh-B\'enard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in…
We consider arbitrary, possibly turbulent, Boussinesq flow which is smooth below a dissipative scale $l_d$. It is demonstrated that the stability of the flow with respect to growth of fluctuations with scale smaller than $l_d$ leads to a…
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…
We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with…
In this paper we establish some regularity criteria for the 3D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. We also obtain some uniform estimates for the corresponding 2D case when the fluid viscosity…
We study turbulent Rayleigh-B\'enard convection through direct numerical simulations in a three-dimensional plane layer of aspect ratio 4 for Rayleigh numbers $10^5 \leq Ra \leq 10^{11}$ and Prandtl number $Pr=0.7$. We summarize the…
This paper examines the stability threshold at high Reynolds numbers $\textbf{Re}$ for the three-dimensional Boussinesq equations with rotation on the domain $\Omega=\{(x,\,y,\,z)\in \mathbb{T} \times \mathbb{R} \times \mathbb{T}\}$ around…
Raylaigh-Benard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of…
Motivated by the need for energetically consistent climate models, the Boussinessq-Coriolis (BC) equations are studied with a focus on the averaged vertical heat transport, ie the Nusselt number. A set of formulae are derived by which…