Numerical investigation of instabilities in three-dimensional skewed shear layers

Vortex development in skewed three-dimensional shear layers has been investigated using Direct Numerical Simulations (DNS). A highly accurate incompressible Navier-Stokes code for computing wall-bounded shear flows has been adapted to the present flow geometry and has been validated for select test cases. As a prototypical laminar base flow for the calculations, a spatially developing Blasius shear layer with a cross-flow component is employed. Due to the inflection point in the skewed velocity profile, inflectional instabilities arise leading to the development of streamwise or oblique vortical disturbances from small-amplitude perturbations depending on the free-stream skew angles. In experiments, these disturbances develop into interesting patterns of vortices with the merging of neighboring streamwise aligned vortices for some configurations, or diamond shaped vortex patterns for others. In the present study, the initial linear growth of the vortical disturbances is studied first using a linearized version of the Navier-Stokes code and simulation results are compared with results from Linear Stability Theory (LST). Small-amplitude disturbances experience rapid linear growth in downstream direction and reach large amplitudes within a short streamwise distance. The nonlinear development and interaction of the vortical disturbances into oblique vortices is studied using the fully nonlinear version of the Navier-Stokes code. Special focus is on the mechanisms leading to the merging of streamwise vortices in symmetric skewed shear layers.