A Theory for the Energy Spectrum of Shear-Dependent Turbulence

Abstract

A theory for the three-dimensional energy spectrum of nearly isotropic shear-dependent turbulence is presented. This theory is based on the author's general model for shear-dependent turbulence and a modified Pao spectral transfer theory which accounts for the effects of viscous loss, shear production, and inertial and velocity gradient transfer in nonstationary turbulence. The resultant spectral transfer equation is solved in closed form for the case of complete similarity. The small wavenumber stationary energy spectrum is shown to vary as k4. The small wavenumber nonstationary solution varies as k6, where ? can have values from 1?4. One-dimensional spectra are computed numerically and compared with the turbulence spectra observed for wind tunnel turbulence with a wide range of Reynolds numbers. The theory successfully predicts several features of the observed spectra at both high and low wavenumbers as well as in the inertial region.