Nonlinear Optimal Disturbances in Compressible Shear Flows

Abstract

We present a variational method for the computation and analysis of nonlinear optimal perturbations in compressible flows. The method is verified in parallel periodic pipe flow at \\(Re = 1750\\) and \\(Ma = 0.20\\). At low initial perturbation energy, the computed perturbations recover the results of linear transient growth analyses. At higher amplitudes, nonlinear effects become relevant, leading to higher energy gains which match the results for incompressible shear flows.