A numerical study of 2-D turbulence

Abstract

A simulation of 2-D turbulence in a square region with periodic boundary conditions has been performed using a highly accurate approximation of the inviscid Navier-Stokes equations to which a modified viscosity has been added. A series of flow pictures show how a random initial vorticity distribution quickly assumes a stringlike pattern which persists as the flow simplifies into a few "cyclones" or "finite area vortex regions". This trend towards well-defined large-scale structures can make it questionable if the 2-D flow should be described as "turbulent" and it casts some doubts on the concept of inertial range and the relevance of energy spectra. The change in appearance seems to be associated with a buildup of phase correlations in the Fourier representation of the vorticity field. During this initial buildup, the energy spectrum seems to follow a k-3-law, but this behavior does not persist. If there is a power law for steady turbulence the results suggest that is more likely to be a k-4-law. © 1977.