Rapid distortion of turbulent structures

A simple two scale rapid distortion model of turbulence is used to investigate the generation of coherent structures and to explain some dynamical effects (vorticity alignment with the intermediate eigenvector of the rate of strain, and vorticity production) which have been observed in recent Direct Numerical Simulations (Vincent & Meneguzzi 1991, Ashurstet al. 1987).A three dimensional homogeneous, isotropic, turbulent velocity field with the Von Karman energy spectrum is generated from random Fourier modes (Kinematic Simulation), and dynamics are added by subjecting this flow to a variety of plane large scale distortions calculated using Rapid Distortion Theory (RDT). Five non-overlapping zones (eddy, donor, convergence, shear and streaming regions) are defined. Eddy, convergence and donor regions increase with the proportion of rotational straining by the large scales, while stream regions increase with irrotational distortion. Shear regions show the largest overall change in volume.After large scale irrotational straining the small scale vorticity aligns with themiddle eigenvector of the small scale rate of strain, but with the largest eigenvector of the large scale rate of strain. There is no net production (destruction) of vorticity except under large scale irrotational strain in regions with two positive (negative) eigenvalues of the small scale rate of strain. These vorticity alignment and production results may be deduced analytically from Rapid Distortion by assuming that the initial turbulence is homogeneous and isotropic.