Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves

We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincidence condition first proposed by Kulikowskii [J. Appl. Math. Mech. 30, 180 (1966)JAMMAR0021-892810.1016/0021-8928(66)90066-9] which takes into account instability wave reflection within the cavity. The analysis yields a set of discrete, nonharmonic frequencies, which compare well with experimental results [Phys. Fluids 20, 114101 (2008)PHFLE61070-663110.1063/1.3005435; Exp. Fluids 50, 905 (2010)EXFLDU0723-486410.1007/s00348-010-0942-9].