Small scale structure of homogeneous turbulent shear flow

Abstract

The structure of homogeneous turbulent shear flow is studied using data generated by direct numerical simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the rapid distortion theory (RDT) limit is approached. Analytical solutions are found for the inviscid compressible RDT equations at long times. The RDT equations are also solved numerically for both inviscid and viscous cases. The RDT solutions, confirmed by the DNS results, show that the even order transverse derivative moments of the dilatational and solenoidal velocity fields are anisotropic, with the dilatational motions more anisotropic than their solenoidal counterparts. The results obtained for the incompressible case are similar to those obtained for the solenoidal motions in the compressible case. The DNS results also indicate an increase in the anisotropy of the even order transverse derivative moments with the order of the moment, in agreement with the RDT predictions. Although the anisotropy decreases with Reynolds number, it is likely that for higher even order moments it will persist at large values of the Reynolds number, in contrast with the postulate of local isotropy. The RDT solutions also predict that the normalized odd order transverse derivative moments of the solenoidal velocity for the compressible case and of the velocity for the incompressible case should approach a constant different than zero at large times. This prediction is supported by the DNS data. For higher odd order normalized moments, the RDT analysis suggests that the anisotropy may persist at large values of the Reynolds number, in agreement with the existent experimental data. The amplification of the dilatational kinetic energy in the direction of the mean shear and the anisotropy of the dilatational dissipation tensor found in the DNS results are also consistent with the RDT analysis.