Nonlinear transient growth in compressible pipe flow

A variational method for flow optimization based on the nonlinear compressible Navier-Stokes equations is presented. The framework allows the identification of finite-amplitude optimal perturbations which maximize the growth of perturbation kinetic energy via a semi-norm formulation. The method is applied in the analysis of nonlinear effects on the transient amplification of disturbances in pipe flow at subsonic Mach numbers. We consider spatially localized perturbations that are restricted to the inflow of the simulation domain. As such, the approach allows direct comparisons to experiments and simulations which commonly introduce disturbances into the flow at a given downstream position. Time integration of the adjoint equations is facilitated via a check-pointing method. The spatial discretization is based on fourth order finite differences on a curvilinear cylindrical grid. The computed perturbations are compared to linearly optimal disturbances which generate streamwise streaks by means of the lift-up mechanism.