On the linear stability of turbulent plane strain flow in a rotating frame
Journal
Physics of Fluids
Date Issued
July 25, 2007
DOI
10.1063/1.2750683
Abstract
We apply inviscid rapid distortion theory to the limiting hyperbolic case of turbulent plain strain flow in a rotating frame and investigate the dependence of the evolution of the turbulent kinetic energy on the frame rotation rate. We derive an analytical two-dimensional solution that, unlike previous oversimplified pressureless analyses, allows for an accurate approximation of the three-dimensional initially isotropic problem. From the analytical solutions, we determine the correct stability criterion for the evolution of the turbulent kinetic energy in this flow. Also, we calculate the asymptotic states of the turbulence, in terms of the normalized Reynolds stresses and structure dimensionality tensor components, which coincide with the exact three-dimensional numerical results.