Spectral Energetics of a Quasilinear Approximation in Uniform Shear Turbulence

Abstract

The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the mean are fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascade is shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. Finally, the QL model is shown to generate anisotropic turbulence throughout the entire wavenumber space and inhibit the nonlinear regeneration of streamwise vortices in the self-sustaining process.