For arbitrary Rayleigh number, Ra, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck-Boussinesq system is proved. We show nonlinear stability for large values of the aspect ratio and {Ra}<{Ra}_L, for some number {Ra}_L which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio, Ra}_L approaches the critical Rayleigh number for the stability of the rest state solution of a suitable linear problem.
Theoretical results on steady convective flows between horizontal coaxial cylinders
PASSERINI, Arianna;FERRARIO, Carlo;
2011
Abstract
For arbitrary Rayleigh number, Ra, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck-Boussinesq system is proved. We show nonlinear stability for large values of the aspect ratio and {Ra}<{Ra}_L, for some number {Ra}_L which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio, Ra}_L approaches the critical Rayleigh number for the stability of the rest state solution of a suitable linear problem.File in questo prodotto:
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