A Numerical Study of 2D Turbulence
Abstract
A simulation of 2D turbulence in a square region with periodic boundary conditions has been performed using a highly accurate approximation of the inviscid NavierStokes 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 welldefined largescale structures can make it questionable if the 2D 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 1977
 DOI:
 10.1016/00219991(77)900237
 Bibcode:
 1977JCoPh..25....1F
 Keywords:

 Energy Spectra;
 Numerical Flow Visualization;
 Stream Functions (Fluids);
 Turbulent Flow;
 Two Dimensional Flow;
 Vorticity;
 Computerized Simulation;
 Fourier Transformation;
 Graphs (Charts);
 NavierStokes Equation;
 Reynolds Number;
 Viscosity;
 Fluid Mechanics and Heat Transfer