OSCILLATORY INSTABILITIES OF A VISCOELASTIC FLUID IN A FLUID-POROUS SYSTEM WITH THE EFFECT OF A MAGNETIC FIELD

The oscillatory instability in a fluid layer overlying a porous layer saturated with the same Oldroyd-B fluid in the presence of a vertical magnetic field is investigated. The Navier-Stokes equation and the modified Darcy's model are employed to describe the hydrodynamic dynamics in the fluid-porous system. The linear stability analysis and the Chebyshev collocation method are used to obtain the numerical results. The influences of the depth ratio, the magnetic field, and viscoelastic properties on oscillatory instability are mainly considered for the Oldroyd-B fluid in the paper. It is found that the depth ratio of the fluid layer and of porous layer and the Chandrasekhar number have opposite effects on convective instabilities. Moreover, a greater depth ratio makes the bimodal nature of neutral curves of the fluid-porous system vanish. The effects of viscoelastic properties of the Oldroyd-B fluid on oscillatory instabilities and the dominant branches are also discussed in detail.