NONLINEAR STABILITY PROBLEM OF A ROTATING DOUBLY DIFFUSIVE FLUID LAYER

The Lyapunov direct method is applied to study the non-linear conditio nal stability problem of a rotating doubly diffusive layer of a Newton ian fluid. For Prandtl number greater than or equal to one and for a c ertain range of Taylor number, a coincidence between the linear and no n-linear (energy) stability thermal Rayleigh number values is found. I t is noted that as the value of the solute Rayleigh number or the Tayl or number increases the coincidence domain between the two theories de creases. For Prandtl number less than one, overall predictions appear to be qualitatively similar to those stated above except that, in this case, the coincidence of thermal Rayleigh number between linear and n on-linear theories is only for very small Taylor and solute Rayleigh n umbers.