On the limitations of linear growth rates in triply diffusive convection in porous medium

The present paper purports to deal with the problem of triply diffusive convection in sparsely distributed porous medium using the Darcy-Brinkman model. Bounds are derived for the modulus of the complex growth rate p of an arbitrary oscillatory perturbation of growing amplitude, neutral or unstable for this configuration of relevance in oceanography, geophysics as well as in many engineering applications. These bounds are obtained by deriving the integral estimates for the various physical quantities by exploiting the coupling between them in the governing equations; and are important especially when at least one boundary is rigid so that exact solutions in the closed form are not obtainable. It is further proved that the result obtain herein is uniformly valid for any combination of rigid and dynamically free boundaries.