I have developed a 3D resolvent code that relies on routines of a CFD code — there is no need to “manually” linearised the equations (more details our paper, section 3.3). With this new tool, we computed the optimal forcing and response in a supersonic flat-plate boundary layer flow. The optimal forcing triggers the largest linear energy growth in a flow at given frequency, through both modal and non-modal effects. Furthermore, non-parallel effects of the base flow are embedded in this approach. This makes it a powerful tool to examine instabilities in shear flows as more physics is retained than in classical linear stability analysis. Note that, in this context, resolvent analysis can also be linked to control theory, which makes it an interesting tool for industrial applications.

More details in our JCP paper.

Optimal response from resolvent analysis in a supersonic boundary layer at Mach number M=4.5. Iso-surface of the streamwise velocity of the perturbations, at -10% and 10% of the maximum absolute value, are shown in red and blue.