Abstract

We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show how many convection cells will be found in the porous layer. The number of cells is shown to depend critically upon the ratio of vertical to horizontal permeability, upon the Brinkman coefficient, and upon the upper boundary condition for the velocity which may be of Dirichlet type or constant pressure. The critical Rayleigh numbers and wave numbers are determined, and it is shown how an unconditional threshold for nonlinear stability may be derived.

Highlights

• Shows how number of convection cells depends upon the temperature of the upper layer and the anisotropy of the permeability

• Shows how number of convection ceels depends upon the temperature of the upper layer and the Brinkman coefficient

• Shows how number of convection cells patters depends upon the upper boundary condition on the velocity or the ambient pressure

中文翻译：

---

各向异性和边界条件对达西和布林克曼多孔穿透对流的影响

摘要

我们研究了各向异性渗透率和边界条件变化对达西型和布林克曼型多孔介质中渗透对流开始的影响。注意力集中在关键特征函数上，它显示了在多孔层中会发现多少对流单元。显示单元的数量主要取决于垂直渗透率与水平渗透率的比率、布林克曼系数以及速度的上边界条件，速度可能是狄利克雷类型或恒压。确定了临界瑞利数和波数，并显示了如何导出非线性稳定性的无条件阈值。

强调

• 显示对流单元的数量如何取决于上层的温度和渗透率的各向异性

• 显示对流单元的数量如何取决于上层的温度和布林克曼系数

• 显示对流单元模式的数量如何取决于速度或环境压力的上边界条件