Linear instability of the lid-driven flow in a cubic cavity

Primary instability of the lid-driven flow in a cube is studied by a linear stability approach. Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. It is shown that Krylov vectors required for application of the Newton and Arnoldi iteration methods can be evaluated by the SIMPLE procedure. The finite volume grid is gradually refined from 100 ³ to 256 ³ nodes. The computations result in grid converging values of the critical Reynolds number and oscillation frequency that allow for Richardson extrapolation to the zero grid size. Three-dimensional flow and most unstable perturbations are visualized by a recently proposed approach that allows for a better insight into the flow patterns and appearance of the instability. New arguments regarding the assumption that the centrifugal mechanism triggers the instability are given for both cases.