Thermohaline convection in a sparsely packed porous medium is studied due to horizontal magnetic field, using both linear and weakly nonlinear stability analyses. The Darcy–Lapwood–Brinkman (DLB) model is employed as the momentum equation. In the linear stability analysis, the normal mode technique is used to find the thermal critical Rayleigh number which is a function of q, Da, \(\Lambda \), \(R_2\) and L. In the weakly nonlinear analysis, a nonlinear two-dimensional Landau–Ginzburg (LG) equation is derived at the onset of stationary convection and the secondary instabilities and heat transport by convection are studied. Coupled one-dimensional LG equations are derived at the onset of oscillatory convection, and the stability regions of steady state, standing waves and travelling waves are studied.

由于水平磁场，使用线性和弱非线性稳定性分析研究了稀疏填充多孔介质中的温盐对流。Darcy-Lapwood-Brinkman (DLB) 模型用作动量方程。在线性稳定性分析中，常模技术用于找到热临界瑞利数，它是q、Da、\(\Lambda \)、\(R_2\)和L的函数. 在弱非线性分析中，在固定对流开始时导出非线性二维朗道-金茨堡 (LG) 方程，并研究了二次不稳定性和对流热传递。在振荡对流开始时导出耦合的一维LG方程，并研究了稳态、驻波和行波的稳定区域。