Convective instability of Ekman boundary layer flow of a Newtonian fluid over a stretchable rotating disk

Abstract

ABSTRACT This paper examines a linear convective instability of an incompressible, Newtonian, viscous fluid rotating over a stretchy spinning disk in an Ekman boundary layer flow. First time in the literature, a numerical analysis of impacts of the stretching mechanism on the stability of the Ekman flow in the presence of the Coriolis force has been carried out, where the bottom disk is allowed to uniformly extend in radial direction. The von Kármán similarity transformations have been used to convert the governing equations of motion into a system of non-linear coupled ordinary differential equations (ODEs) in non-dimensional variables. Then velocity profiles of the flow have been obtained by numerically solving these dimensionless ODEs. The neutral stability curves were then obtained by performing a linear stability analysis for the convective mechanism by using the Chebyshev collocation method. Surface stretching has a globally stabilizing influence on both Type-I and Type-II instability modes of the Ekman flow, according to the stability curves. Then, the result established from the stability curves has been verified by calculating total kinetic energy change due to induced perturbations in the flow system. y.