Linear stability analyses of natural convection flows in a differentially heated square cavity with conducting horizontal walls

The stability of two-dimensional (2D) natural convection flows with respect to both two- and three-dimensional perturbations is investigated numerically. Several methods (Arnoldi’s method, preconditioned Newton’s iteration and preconditioned continuation method) are put together for this purpose and applied to natural convection in a differentially heated square cavity with conducting horizontal walls for a large range of Prandtl numbers. These methods are first validated by comparison with results reported in the literature for several Prandtl numbers for both two-dimensional and three-dimensional perturbations. They are then used to extend the stability of the 2D base flows to two-dimensional perturbations for other Prandtl numbers, and to investigate in detail the stability of these two-dimensional base solutions with respect to three-dimensional perturbations for a large range of Prandtl number. For Prandtl number equal to 1 the base solutions are more unstable to three-dimensional perturbations and t...

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