An analytical solution for rapidly distorted turbulent shear flow in a rotating frame

Abstract

In this study we apply rapid distortion theory to the case of nonstratified homogeneous turbulence that is sheared in a frame that counter-rotates at a rate that matches in magnitude the rotation associated with the mean shear. In the inviscid case, analytical solutions are worked out for the evolution of the components of the Reynolds stresses and the structure dimensionality tensor, and these are shown to equal each other. The results are compared to direct numerical simulations data with which they proved to be in good agreement, especially in terms of the Reynolds shear stress and of the dimensionless tensor components. Finally, the development of the structure of a passive scalar field with a constant mean gradient is investigated, and remarkable analogies are shown to exist between this case and the case of shear in a fixed frame.