Decaying 2D Turbulence in Bounded Domains: Influence of the Geometry

Abstract

We present direct numerical simulation of two-dimensional decaying turbulence in wall bounded domains. The Navier-Stokes equations are solved in a periodic square domain using the vorticity-velocity formulation. The bounded domain is imbedded in the periodic domain and the no-slip boundary conditions on the wall are imposed using a volume penalisation technique. The numerical integration is done with a Fourier pseudo-spectral method combined to a semi-implicit time discretization with adaptive time stepping. We study the influence of the geometry of the domain on the flow dynamics and in particular on the long time behaviour of the flow. We consider different geometries, a circle, a square, a triangle and a torus and we show that the geometry plays a crucial role for the decay scenario.