Synthesis of homogeneous anisotropic divergence-free turbulent fields with prescribed second-order statistics by vortex dipoles

This Communication presents a mathematical procedure for generation of turbulent velocity fields with prescribed shell-summed energy spectra. The velocity field is represented as the sum of velocities induced by a set of randomly distributed vortex dipoles (vortons). Closed-form analytical solutions are found for the inner structure of the vortons from the condition that the shell-summed energy spectrum of the synthesizing field is equal to the prescribed one. The proposed procedure is applied to turbulent fields with the spectrum of the decaying turbulence and the typical velocity energy spectrum of homogeneous turbulence. The solution for decaying turbulence is the exact analytical solution of the Navier-Stokes equation for the turbulent field in the final stage of the decay. (c) 2007 American Institute of Physics.