Non-linear disturbance mechanisms of transitional shock wave-boundary layer interactions*

Most existing stability methods employed to unravel the laminar-to-turbulence transitional mechanisms in shock wave-boundary layer interactions are linear and therefore limited to the early transitional stages.

In order to account for non-linearity in an efficient and tractable way, we project the governing Navier-Stokes on a finite and small number of temporal and spatial harmonics which non-linearly interact transferring energy among them and with the mean flow. The proposed method, termed Space-Time Spectral Method (STSM), enables the computation of worst-case disturbances through non-linear optimization, and performing parametric studies efficiently.

We apply the STSM framework to a Mach 2.15 oblique shock reflection. In the absence of global instabilities, the worst-case transition is initiated by Kelvin-Helmholtz waves which then interact non-linearly to produce streamwise vortices downstream of the separation zone. As a consequence, streaky structures emerge and later break down to turbulence.

By analyzing also globally unstable interactions, we provide a comprehensive physical understanding and prediction of the transition process to turbulence in shock-wave boundary layer interactions.