Characterization Of Rivlin-Ericksen Viscoelastic Fluid In The Presence Of Rotation In A Porous Medium

A layer of Rivlin-Ericksen viscoelastic fluid heated from below in a porous medium is considered in the presence of uniform vertical rotation. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical rotation in a porous medium, opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime , where is the Taylor number; and is the medium permeability. The result is important since it hold for all wave numbers and for rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form, is not obtainable.