Nonlinear stability problem of a rotating doubly diffusive fluid layer. (English) Zbl 0899.76181
Summary: The Lyapunov direct method is applied to study the nonlinear conditional stability problem of a rotating doubly diffusive layer of a Newtonian fluid. For Prandtl number greater than or equal to one and for a certain range of Taylor number, a coincidence between the linear and nonlinear (energy) stability thermal Rayleigh number values is found. It is noted that as the value of the solute Rayleigh number or the Taylor number increases the coincidence domain between the two theories decreases. For Prandtl number less than one, overall predictions appear to be qualitatively similar to those stated above except that, in the case, the coincidence of thermal Rayleigh number between linear and nonlinear theories is only for very small Taylor and solute Rayleigh numbers.
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