A MODEL FOR LARGE-SCALE STRUCTURES IN TURBULENT SHEAR FLOWS

A procedure based on energy stability arguments is presented as a meth od for extracting large-scale, coherent structures from fully turbulen t shear flows. By means of two distinct averaging operators, the insta ntaneous flow field is decomposed into three components: a spatial mea n, coherent held and random background fluctuations. The evolution equ ations for the coherent velocity, derived from the Navier-Stokes equat ions, are examined to determine the mode that maximizes the growth rat e of volume-averaged coherent kinetic energy. Using a simple closure s cheme to model the effects of the background turbulence, we find that the spatial form of the maximum energy growth modes compares well with the shape of the empirical eigenfunctions given by the proper orthogo nal decomposition. The discrepancy between the eigenspectrum of the st ability problem and the empirical eigenspectrum is explained by examin ing the role of the mean velocity field. A simple dynamic model which captures the energy exchange mechanisms between the different scales o f motion is proposed. Analysis of this model shows that the modes whic h attain the maximum amplitude of coherent energy density in the model correspond to the empirical modes which possess the largest percentag e of turbulent kinetic energy. The proposed method provides a means fo r extracting coherent structures which are similar to those produced b y the proper orthogonal decomposition but which requires only modest s tatistical input.