A MATHEMATICAL THEOREM IN ROTATORY THERMOHALINE CONVECTION

The present paper mathematically establishes that rotatory thermohalin e convection of the Veronis type cannot manifest as oscillatory motion of growing amplitude in an initially bottom heavy configuration if th e thermohaline Rayleigh number R(s), the Lewis number tau, and the Pra ndtl number sigma satisfy the inequality R(s) less than or equal to 27 /4 pi(4) (1 + tau/sigma). It further establishes that this result is u niformly valid for the quite general nature of the bounding surfaces, thus achieving a rotatory extension of that important characterization theorem of Banerjee et al. [2] on the nonrotatory hydrodynamic proble m. A similar characterization theorem is stated only for rotatory ther mohaline convection of the Stern type and its mathematical validity wi ll be shown in detail elsewhere, (C) 1995 Academic Press, Inc.