Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Abstract

Theoretical analyses of pressure related turbulent statistics are vital for a reliable and accurate modeling of turbulence. In the inertial subrange of turbulent shear flow, pressure–velocity and pressure–strain correlations are affected by anisotropy imposed at large scales. Recently, Tsuji and Kaneda (2012 J. Fluid Mech. 694 50) performed a set of experiments on homogeneous shear flow, and estimated various one-dimensional pressure related spectra and the associated non-dimensional universal numbers. Here, starting from the governing Navier–Stokes dynamics for the fluctuating velocity field and assuming the anisotropy at inertial scales as a weak perturbation of an otherwise isotropic dynamics, we analytically derive the form of the pressure–velocity and pressure–strain correlations. The associated universal numbers are calculated using the well-known renormalization-group results, and are compared with the experimental estimates of Tsuji and Kaneda. Approximations involved in the perturbative calculations are discussed.