On the Bounds for Oscillation in Thermohaline Convection Problems with Temperature-Dependent Viscosity
Dhiman Joginder Singh1,*, Sharma Poonam1, Goyal Megh Raj2
1Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005 (H.P.) India
2Department of Mathematics, D.A.V. College, Malout-152107, Punjab, India
*Corresponding Author: firstname.lastname@example.org
The present paper extends the analysis of Gupta et al. (2001, J. Math. Anal. Appl., 264, 398) of Veronis and Stern type's thermohaline convection problems for the case of temperature-dependent viscosity. The stability of the oscillatory motions for both types of problems with variable viscosity is discussed in this paper and the upper bounds for the growth rates for neutral or unstable oscillatory perturbations are also prescribed. The obtained results are uniformly valid for all combination of dynamically free and rigid boundaries and are free from a curious condition on the non-negativity of the second derivative of viscosity parameter. Further, various results for an initially top-heavy as well as an initially bottom heavy configurations follow as consequence.
Thermohaline convection, oscillatory motions, complex growth rate, temperature-dependent viscosity, eigenvalue problem.