On the Modulation of Oscillation in Thermohaline Convection Problems Using Temperature Dependent Viscosity

Abstract

Abstract. The present paper mathematically investigates the effect of temperature dependent viscosity on the onset of instability in thermohaline convection problems of Veronis and Stern type configurations, using linear stability theory. A sufficient condition for the stability of oscillatory modes for thermohaline configuration is derived. When the compliment of this sufficient condition is true, the oscillatory motions of neutral or growing amplitude may exist, and hence the bounds for the complex growth rate of these neutral or unstable modes are derived, when viscosity of the fluid is an arbitrary function of temperature. Some general conclusions for the cases of linear and exponential variations of viscosity are worked out. The present analysis thus shows that the oscillations in thermohaline convection problems can be modulated or arrested by considering the temperature dependent viscosity of the fluid.