Transient Growth in Hypersonic Boundary Layers

Abstract

This paper investigates the relative importance of modal and non-modal growth mechanisms in flat-plate, hypersonic boundary layers as well as the effects of Mach number and wall cooling on these processes. Optimal disturbances are calculated in both the spatial and temporal frameworks using an eigenvector decomposition of the locally-parallel, linearized Navier-Stokes equations. It is found that for every Mach number there is an optimal level of wall cooling that minimizes transient growth; at this condition the wall temperature is slightly below the freestream temperature, with lower wall temperatures needed as the Mach number increases. The competition between modal and non-modal growth mechanisms is examined over a range of Reynolds numbers by calculating N factor curves for both processes. For conditions relevant to high enthalpy flows (high Mach number, cold wall), transient growth is rapidly overtaken by modal instabilities while the level of amplification remains small. At lower Mach numbers or adiabatic conditions, the transient growth is overtaken more slowly. For low supersonic Mach numbers and cold walls there are no modal instabilities, but the level of non-modal amplification is increased such that the initiation of transition by infinitesimal perturbations is plausible despite the absence of modal instabilities.