Abstract A weakly nonlinear analysis is performed on the classical Darcy-Benard problem to determine the effects of local thermal nonequilibrium on the planform of convection immediately post-onset. It is found that two-dimensional rolls are always favoured. Although disturbances which are perpendicular to the roll whose stability is being assessed usually form the most dangerous mode of instability, it is also found that there are regions of parameter space where the cross-roll instability becomes inoperative as an instability mechanism.

中文翻译：

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具有局部热非平衡的 Darcy-Bénard 对流模式选择

摘要 对经典的 Darcy-Benard 问题进行了弱非线性分析，以确定局部热非平衡对发生后立即对流平面的影响。发现二维卷总是受欢迎的。虽然垂直于正在评估稳定性的滚动的扰动通常形成最危险的不稳定模式，但也发现存在参数空间的区域，其中横向滚动不稳定性作为不稳定机制变得不起作用。