Oberbeck--Boussinesq 近似与 Rayleigh--Benard 对流再探

带牛顿引力场的Oberbeck-Boussinesq系统的大自相似解

Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field

本文研究全三维空间中带牛顿引力场的Oberbeck-Boussinesq耦合系统，利用Leray-Schauder定理与紧性论证构造了无需齐次初值小性假设的大自相似解。

The Oberbeck--Boussinesq Approximation as a Constitutive Limit

We derive the usual Oberbeck--Boussinesq approximation as a constitutive limit of the full system describing the motion of an compressible linearly viscous fluid. To this end the starting system is written, using the Gibbs free energy, in the variables $\mathbf v, θ$ and $p$. The Oberbeck--Boussinesq system is then obtained as the thermal expansion coefficient $α$ and the isothermal compressibility coefficient $β$ tend to zero.

含非局域温度项的磁-奥伯贝克-博辛内斯克近似的严格推导

Rigorous derivation of magneto-Oberbeck-Boussinesq approximation with non-local temperature term

针对可压缩导磁流体系统，分析小马赫数等参数下的行为，严格推导得到含非局域温度项的修正磁-奥伯贝克-博辛内斯克系统，并明确平行板区域的流动与磁场特性。

Oberbeck-Boussinesq近似的严格推导揭示意外项

Rigorous derivation of the Oberbeck-Boussinesq approximation revealing unexpected term

本文在低Mach和Froude数机制下严格推导可压缩粘性导热流体的渐近极限，发现其表现为带温度偏差非局部边界条件的Oberbeck-Boussinesq系统。

一个适用于非弹性 Oberbeck-Boussinesq 系统的 Lorenz 模型

A Lorenz Model for an Anelastic Oberbeck-Boussinesq System

本文针对含可压缩性的非弹性 Oberbeck-Boussinesq 系统，通过分析其 Lorenz 近似系统，证明了静止状态在 Bénard 问题中具有更高的稳定性，即对流起始需要更高的临界 Rayleigh 数。

Oberbeck-Boussinesq流体流动的随机涡量与膨胀率模型

Random vortex and expansion-rate model for Oberbeck-Boussinesq fluid flows

本文通过涡量和膨胀率表述建立新的积分表示，提出随机涡方法数值求解Oberbeck-Boussinesq可压缩流动，实验成功捕捉Bénard对流并揭示密度与膨胀率动力学信息。

Existence, Uniqueness, Analyticity, and Borel Summability of Boussinesq and Magnetic Benard Equations

Through Borel summation methods, we analyze two different variations of the Navier-Stokes equation --the Boussinesq equation and the magnetic Benard equation. This method has previously been applied to the Navier-Stokes equation. We prove that an equivalent system of integral equations in each case has a unique solution, which is exponentially bounded for p in R^{+}, p being the Laplace dual variable of 1/t. This implies the local existence of a classical solution in a complex t-region that includes a real positive time (t)-axis segment. In this formalism, global existence of PDE solutions bec…

关于带耗散加热的广义Navier--Stokes--Fourier系统解的存在性

On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating

针对高温度梯度下Oberbeck--Boussinesq系统的不足，研究带耗散加热的广义Navier--Stokes--Fourier系统，证明其耗散适宜弱解的大数据长时间存在性，为后续稳定性分析奠定基础。

Ergodicity in Randomly Forced Rayleigh-Bénard Convection

We consider the Boussinesq approximation for Rayleigh-Bénard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two space dimensions, with sufficient stochastic forcing in the temperature component and large Prandtl number, we establish the existence of a unique ergodic invariant measure. In three space dimensions, we prove the existence of a statistically invariant state, and establish unique ergodicity for the infinite Prandtl Boussinesq system. Throughout this work we provide streamlined proofs of unique ergodicity which invoke an …

Local well-posedness for Benard convection without surface tension

We consider the Bénard convection in a three-dimensional domain bounded below by a fixed flatten boundary and above by a free moving surface. The domain is horizontally periodic. The fluid dynamics are governed by the Boussinesq approximation and the effect of surface tension is neglected on the free surface. Here we develop a local well-posedness theory for the equations of general case in the framework of the nonlinear energy method. \end{abstract}

Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media

We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bénard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in $L^2$ and $H^1$. Eventually, we comment on the applicability of a data assimilation algorithm to our system.

On the Boussinesq equations with non-monotone temperature profiles

In this article we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles $T(y)$. As a first main result we show that if $T'$ is of size at most $ν^{1/3}$ in a suitable norm, then the linearized Boussinesq equations with only vertical dissipation of the velocity but not of the temperature are stable. Thus, mixing enhanced dissipation can suppress Rayleigh-Bénard instability in this linearized case. We further show that these results extend to the (forced) nonlinear equations with vertica…

关于旋转流体的Rayleigh–Bénard对流问题

On the Rayleigh--B\' enard convection problem for rotating fluids

本文证明标准Oberbeck–Boussinesq近似无法作为旋转坐标系中Navier–Stokes–Fourier系统的奇异极限获得，挑战了传统热驱动流体模型。

Limitations of the background field method applied to Rayleigh-Bénard convection

We consider Rayleigh-Bénard convection as modeled by the Boussinesq equations, in case of infinite Prandtl number. There is a broad interest in bounds of the upwards heat flux, as given by the Nusselt number ${\rm Nu}$, in terms of the forcing via the imposed temperature difference, as given by the Rayleigh number in the turbulent regime ${\rm Ra}\gg 1$. In several works, the background field method applied to the temperature field has been used to provide upper bounds on ${\rm Nu}$ in terms of ${\rm Ra}$. In these applications, the background field method comes in form of a variational proble…

水平环域中的自然对流：稳态问题的临界瑞利数

Natural convection in the horizontal annulus: critical Rayleigh number for the steady problem

本文研究水平环域中二维 Oberbeck-Boussinesq 系统基本流失稳的临界瑞利数，通过构造泛函分析框架和数值格式实现求解。