TITLE:
On the Stationary Convection of Thermohaline Problems of Veronis and Stern Types
AUTHORS:
Joginder S. Dhiman, Praveen K. Sharma, Poonam Sharma
KEYWORDS:
Thermohaline Convection, Stationary Convection, Eigenvalue Problem, Principle of Exchange of Stabilities, Rayleigh Number
JOURNAL NAME:
Applied Mathematics,
Vol.1 No.5,
December
1,
2010
ABSTRACT: The stability of thermohaline convection problems of Veronis and Stern types for stationary convection is studied for quite general nature of boundaries. It is shown by means of an appropriately chosen linear transformation, that in case of stationary convection the equations describing the eigenvalue problem for thermohaline convection problems are identical to equations describing the eigenvalue problem for classical Bénard convection problem. As a consequence, the values of the critical Rayleigh numbers for the onset of stationary convection in thermohaline convection problems are obtained. Also, necessary conditions for the validity of principle of exchange of stabilities for thermohaline convection problems are derived using variational principle.