The two-dimensional Navier-Stokes-Kuramoto-Sivashinsky equation on the Connection Machine

Abstract

The two-dimensional Navier-Stokes equations with a large scale instability of the Kuramoto-Sivashinsky type, describing marginally negative eddy viscosity situations, is simulated on a Connection Machine CM-2. Up to millions of time steps at the resolution 256 2 and tens of thousands at the resolution 1024 2 are performed. A linear growth phase, a disorganized inverse cascade phase and a structured vortical phase are successively observed. In the vortical phase monopolar and multipolar structures are proliferating and display strongly depleted nonlinearities.