The scope of this study is to determine the conditions for the onset of the instability in a horizontal porous layer subject to isoflux boundary conditions and with an infinitely wide single–cell basic flow. When the circulation in the basic cellular flow is absent, one recovers the usual Darcy–Bénard conduction basic state. The governing parameters are the Rayleigh number associated with the uniform wall heat flux, and the dimensionless horizontal temperature gradient. The latter parameter controls the magnitude of the basic cellular circulation flow in the horizontal direction. The modal analysis of the instability is carried out numerically by employing a pseudo–spectral method, as well as the shooting method for the solution of the stability eigenvalue problem. Neutral stability and the critical conditions for the onset of the convective instability of the basic state are investigated.

本研究的范围是确定受等通量边界条件和无限宽单细胞基本流影响的水平多孔层中不稳定的开始条件。当基本细胞流中的循环不存在时，人们会恢复通常的达西-贝纳德传导基本状态。控制参数是与均匀壁面热通量和无量纲水平温度梯度相关的瑞利数。后一个参数控制水平方向基本细胞循环流的大小。不稳定性的模态分析是通过采用伪谱方法以及解决稳定性特征值问题的射击方法进行数值分析的。