On Linear Complex Growth Rate in Rotatory-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium

Thermosolutal convection in a layer of Rivlin-Ericksen viscoelastic fluid of Veronis (1965) type is considered in the presence of uniform vertical rotation in a porous medium. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of Rivlin-Ericksen viscoelastic fluid convection in the presence of uniform vertical rotation, for any combination of free and rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, established that the complex growth rate σ of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside right half of the a semi-circle
σ²_r+σ²_i〈 Maximum of [{T_A(εP₁/P₁+εF)²},{R_s/E'P₃(εP₁/P₁+εF)}]
in the ε_rε_i-plane, where, R_s is the thermosolutal Rayleigh number, T_A is the Taylor number, F is the viscoelasticity parameter, p₃ is the thermosolutal prandtl number, ε is the porosity and P_l is the medium permeability. This prescribes the bounds to the complex growth rate of arbitrary oscillatory motions of growing amplitude in the Rivlin-Ericksen viscoelastic fluid in Veronis (1965) type configuration in the presence of uniform vertical rotation in a porous medium. A similar result is also proved for Stern (1960) type of configuration. The result is important since the result hold for any arbitrary combinations of dynamically free and rigid boundaries.