Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation

Abstract

Detailed comparison of spatial direct numerical simulations (DNS) and secondary linear stability theory (SLST) is provided for the three-dimensional crossflow-dominated boundary layer also considered at the DLR-Göttingen for experiments and theory. Secondary instabilities of large-amplitude steady and unsteady crossflow vortices arising from one single primary mode have been analysed. SLST results have been found to be reliable with respect to the dispersion relation and the amplitude distribution of the modal eigenfunction in the crosscut plane. However, significant deviations have been found in the amplification rates, the SLST results being strongly dependent on the necessarily simplified representation of the primary state. The secondary instability mechanisms are shown to be local, i.e. robust with respect to violations of the periodicity assumption made in the SLST for the wall-parallel directions. Perturbations associated with different local maxima of the spanwise periodic eigenfunctions develop independently from each other interacting only with the primary vortices next to them. Characteristic structures induced by different secondary instability modes have been analysed and an analogy with the Kelvin–Helmholtz instability mechanism has been highlighted.