Twodimensional shear flow turbulence: A statistical theory of vortex filaments
Abstract
A theory of twodimensional free shear flow turbulence is proposed. In particular, the role of interactions of fluctuations with the mean flow is distinguished from that of interactions among fluctuations. The former are responsible for the extraction of free energy necessary for maintaining the turbulence, while the latter lead to the enstrophy cascade which generates smallscale eddies. On the length scales of greatest interest, turbulence is anisotropic because of the influence of mean flow shear. At smaller scales, selfsimilar enstrophy transfer occurs and yields the familiar power law spectrum. Free energy extraction is accompanied by mean flow relaxation. Two distinct mechanisms are involved. In addition to the usual quasilinear diffusion, there is a nonlinear drift which acts to enhance localized fluctuations and flatten the mean flow profile. The saturated state is characterized by collective resonances which must be nonlinearly damped in order to balance their generation by seededdy induction. This balance gives rise to a condition for the determination of the nonlinear damping rate, and thus the turbulence level. The spatial structure of the saturated fluctuations is also predicted.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1987
 Bibcode:
 1987STIN...8810295C
 Keywords:

 Shear Flow;
 Shear Properties;
 Statistical Analysis;
 Turbulent Flow;
 Two Dimensional Flow;
 Free Energy;
 Free Flow;
 Fluid Mechanics and Heat Transfer