Global 2D stability analysis of the cross lid-driven cavity flow with a streamfunction-vorticity approach

We have recenty analyzed the global two dimensional (2D) stability of the staggered lid-driven cavity (LDC) flow with a higher order compact (HOC) approach. In the analysis;cal parameters are deter mined for both the parallel and anti-parallel motion of the lids arid a detailed analysis has been carried out on either side of the critical values. In this article, we carrY out an investigation of fEow stabilities inside a two sided cross lid-driven cavity with a pair of opposite, lids moving in both parallel and anti-parallel directions. On discretization, the governing 2D Navier-Stokes (WS) equations describing the steady flowand flow perturbations results in a generalized eigenvalue problem which s solved for determining the critical parameters on)four diffeent grids. Elaborate computation is performed fora wide range of Reynolds numbers(R e on either side of the critical values in the range 200 <= Re <= 10000. For flows below the critical Reynolds number Re,, our numerical results are, compared with established steady-state results and excellent agreement is obtained in all the cases. For Reynolds numbers above Rec, phase plane and spectral density analysis confirmed the existence of periodic, quasi-periodic, and stable flow patterns