Effects of confinement on absolute and convective instabilities for momentum-driven countercurrent shear layers

Using spatiotemporal linear stability theory, we conduct a systematic study of confined countercurrent shear layer velocity profiles, using realistic velocity profiles that capture the effects of wall boundary layers on canonical profile shapes. It is shown, in line with previous studies, that additional unstable modes are generated when confining walls are present. This leads to shifts in the absolute-convective transition boundary, with the effects being dramatic when confinement is on the high-speed side. However, over large parts of the parameter space, as specified by the counterflow parameter R and the degree of confinement (H, measured in terms of shear layer momentum thickness), these correspond to long wave modes. It is shown that as counterflow parameter R (=U1-U2U1+U2, U1 and U2 being primary and secondary velocity streams) is increased to large values, the confined mode gradually decreases in wavelength. Comparisons of the behavior of the frequency of this confined mode are made with observed peak frequencies from the first experimental realization of momentum-driven confined countercurrent shear layers, and the results are shown to be in reasonable agreement.