The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.

中文翻译：

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多孔介质中的双扩散Soret对流现象：Vadasz惯性项的影响

在包含惯性项的广义达西模型的情况下，研究了热扩散Soret现象在水平多孔层中发生双扩散对流的开始。通过最近在Rionero中引入的线性化原理（Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28：21–47，2017），证明了热-溶液传导解的线性和非线性（全局）稳定性阈值之间的一致性。获得了必要的充分条件，以保证以封闭的代数形式开始稳定或振荡对流。