Direct numerical simulation of transient growth on a flat plate at Mach 3

The transient growth phenomenon in three dimensional shear flows has been shown to account for large disturbance growth in cases where traditional stability analyses show limited or no growth. For this reason, transient growth has been put forward as a potential cause of bypass transition. The purpose of the current study is to investigate the presence of non-linear effects as the energy of disturbances increases and their potential role in boundary layer transition on a flat plate in supersonic, compressible flow. An optimal disturbance solver based on linear theory was created and is validated against previously published data. The disturbances generated by this solver are input into a computational fluid dynamics (CFD) solver to model the disturbance evolution in three dimensions. The results from the CFD solver are compared with linear theory to ensure accuracy in the full three-dimensional simulations. Finally, the input energies are increased to investigate the effects of non-linear terms in the governing equations. Results show that a non-dimensional input energy of E_in = 3.024. 10^-3 is required for a departure from linear behavior for the mean flow conditions considered.