On the Orientation of Vortical Structures in Homogeneous Turbulent Shear Flows with Stable Stratification or System Rotation

The orientation of vortical structures in homogeneous turbulent shear flows with stable stratification or system rotation is studied using results from direct numerical simulations. Inclined structures are observed in the plane of shear and the three-dimensional two-point autocorrelation coefficient of vorticity magnitude is computed to quantify their orientation. Isosurfaces of the autocorrelation coefficient closely resemble an ellipsoid with its major axis oriented into the direction of the structures. A least-squares fit of an ellipsoid to the isosurfaces is performed and the major axis is determined. From the major axis, the inclination angle of the structures is computed. The inclination angle is observed to have a similar dependence on the Richardson number Ri, in the case of stratified shear flows, and on the rotation to shear rate ratio f/S, in the case of rotating shear flows, as the growth rate of the turbulent kinetic energy. Therefore, the structure orientation in homogeneous turbulent shear flows appears to be directly related to the dynamics of the flows.