Secondary instabilities of stationary crossflow vortices: Comparison of LST-2D and PSE-3D with DNS

Abstract

Three-dimensional boundary layers over swept wings are susceptible to crossflow instabilitieswhich manifest themselves in the form of both stationary and traveling crossflow vortices. The boundary layer, strongly distorted by the momentum redistribution caused by the stationarycrossflow vortices, is prone to the growth of secondary instabilities which ultimately triggertransition. Major discrepancies between direct numerical simulation (DNS) and stabilitymethodologies have been reported in literature on the development of unsteady perturbationin stationary-crossflow-dominated boundary layers. With the aim of shedding light on theinconsistencies of the two numerical methodologies, a detailed comparison of DNS and linearstability theory, for the evolution of secondary perturbation of stationary crossflow vortices,is provided here. In particular, the linear stability theory (LST-2D) and parabolized stabilityequations (PSE-3D) are employed to study the evolution of such spatial instabilities in boundarylayers characterized by two inhomogeneous directions. An introduction on the formulation ofthe LST-2D and PSE-3D in a non-orthogonal coordinate system is provided and the key aspectof fixing the spatial growth direction is discussed. The growth of the unsteady disturbancesin a boundary layer over a swept wing, which reproduces an experimental setup, is presented.