A Mathematical Theorem in Rotatory Thermohaline Convection

AbstractThe present paper mathematically establishes that rotatory thermohaline convection of the Veronis type cannot manifest as oscillatory motion of growing amplitude in an initially bottom heavy configuration if the thermohaline Rayleigh number Rs, the Lewis number τ, and the Prandtl number σ satisfy the inequality Rs ≤ 274 π4 (1 + τ/σ). It further establishes that this result is uniformly 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 problem. A similar characterization theorem is stated only for rotatory thermohaline convection of the Stern type and its mathematical validity will be shown in detail elsewhere