Rotatory Thermosolutal Convection in a Couple-Stress Fluid

Abstract

The thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Stability Analysis in Couple-Stress Rotatory Fluid

“…Using the boundary conditions (18), it can be shown that all the even order derivatives of must vanish on the boundaries, and hence the proper solution of ( 17) characterizing the lowest mode is…”

“…Proof: Multiplying equation ( 14) by * , the complex conjugate of , integrating over the range of , and making use of equations ( 15) and ( 16) together with the boundary conditions (18), we obtain Equation ( 29) yields that may be positive or negative i.e. there may be stability or instability in the presence of couple-stress parameter, rotation and porous medium.…”

“…Kumar et al [16] have considered the thermal instability of a layer of a couple-stress fluid acted on by a uniform rotation, and have found that for stationary convection, the rotation has a stabilizing effect whereas couple-stress has both stabilizing and destabilizing effects. Thermosolutal convection in a couple-stress fluid in presence of magnetic field and rotation, separately, has been investigated by Kumar and Singh [17,18]. Kumar and Kumar [19] have considered the problem of thermosolutal convection in compressible couple-stress fluid in presence of suspended particles.…”

Thermosolutal convection in a rotating couple-stress uid

“…A lot of theoretical results on couple-stress fluids, taking into account several effects, can be found in [26], where, in the framework of the linearized stability theory, by using the normal modes technique, the thermosolutal convection in a layer of electrically couple stress conducting fluid was considered. In the case of stationary convection a linear instability analysis was performed, obtaining the dispersion relation, also numerically analized.…”

“…The motion which occurs in S , for an observer rotating around the same axis z with the same angular velocity   , in the Oberbeck-Boussinesq approximation, is described by the following equations [1], [24], [26] , )] ( )…”