We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work, we demonstrate that regardless of the size of the Rayleigh number, the perturbation solution will decay exponentially in time for the superdiffusion case. In addition, we establish a similar result for convection in a bidisperse porous medium where both macro- and microporosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.

我们研究了达西多孔材料中对流的完全非线性模型，其中扩散是 Barletta 最近提出的反常类型。分析了完全非线性模型，但我们考虑了可变重力或穿透对流效应，这会导致空间相关系数。即使在线性化情况下，这种空间依赖性通常也需要数值求解。在这项工作中，我们证明，无论瑞利数的大小如何，对于超扩散情况，微扰解都会随时间呈指数衰减。此外，我们还对同时存在宏观和微观孔隙效应的双分散多孔介质中的对流建立了类似的结果。此外，我们还证明了热溶质对流的类似结果。