THERMAL CONVECTION OF RIVLIN-ERICKSEN FLUID IN THE PRESENCE OF VERTICAL ROTATION

The thermal instability of a Rivlin-Ericksen viscoelastic fluid, acted upon by uniform vertical rotation and heated from below, is investigated. Following linearized stability theory and normal mode analysis, the mathematical analysis of the governing equations of Rivlin-Ericksen viscoelastic fluid convection with a uniform vertical rotation is performed. It is shown that for the cases of rigid boundaries the complex growth rate sigma of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle, in the right-hand half of a complex sigma-plane with the center at the origin. This prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in a rotatory Rivlin-Ericksen viscoelastic fluid heated from below. Furthermore, the conditions necessary for the existence of oscillatory motions of growing amplitude in the present configuration and the sufficient condition for the validity of the Principle of Exchange of Stabilities are established.