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We investigate the fully nonlinear model for convection in a Darcy porousmaterial where the diffusion is of anomalous type as recently proposed byBarletta. The fully nonlinear model is analysed but we allow for variablegravity or penetrative convection effects which result in spatially dependentcoefficients. This spatial dependence usually requires numerical solution evenin the linearized case. In this work we demonstrate that regardless of the sizeof the Rayleigh number the perturbation solution will decay exponentially intime for the superdiffusion case. In addition we establish a similar result forconvection in a bidisperse porous medium where both macro and micro porosityeffects are present. Moreover, we demonstrate a similar result forthermosolutal convection.

Asymptotic behaviour for convection with anomalous diffusion