Magneto-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium

摘要

Thermosolutal instability of Veronis type in Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field in a porous medium is considered. 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 any arbitrary combination of free and 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 in the presence of uniform vertical magnetic field in a porous medium, are necessarily non-oscillatory, in the regime where R_s is the Thermosolutal Rayliegh number, Q is the Chandrasekhar number, p_2 is the magnetic Prandtl number, p_3 is the thermosolutal Prandtl number, P_1 is the medium permeability, ε is the porosity and F is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. A similar characterization theorem is also proved for Stem type of configuration.