On the Limitations of Complex Growth Rate in Triply Diffusive Convection in Porous Medium: Darcy-Brinkman Model

Abstract

The paper mathematically establishes that the complex growth rate $(p_r, p_i)$ of an arbitrary, neutral or unstable oscillatory perturbation of growing amplitude in triply diffusive convection analogous to stern type fluid layer heated from below, must lie inside a semicircle in the right half of the $(p_r, p_i)$-plane whose centre is at the origin and radius equals $\frac{1} {E\sigma}\left(\sqrt{\left|R\right|E\sigma-\frac{27}{4}p^{4}}\right)$, where $R$ is the thermal Rayleigh number, s is the Prandtl number,$E$ is a constant. Further this result is uniformly valid for quite general nature of bounding surfaces.