Onset of two-dimensional turbulence with high reynolds numbers in the navier-stokes equations

Abstract

Even though turbulence is a tri-dimensional phenomenon, two-dimensional flows at high Reynolds numbers Re give some clues of transition to real turbulence, mainly through the vorticity. This transition is shown here with flows that are obtained computationally from the unsteady Navier-Stokes equations in stream function and vorticity variables on the well known un-regularized driven cavity problem. The work covers the range of 5000 ≤ Re ≤ 31000; the results are obtained with a numerical scheme based on a fixed point iterative process applied to the elliptic nonlinear system that results after time discretization, it was reported in [1] for lower Re; it started since WCCM V, 2002, [2]-[3], and we are still working on it. The scheme has the ability to start from rest, initially, regardless of Re and has shown to be robust enough to handle high Reynolds numbers, which is not an easy task to deal with.