Ryan Poole

Jets and wakes are fundamental fluid flows that arise in a wide range of environmental and aerospace applications. They are typically studied as open systems. Here we are interested in the implications of placing the jet or wake inside of another system, as well as the implications of compliant walls. In particular, the effect of asymmetry is considered on the absolute instability properties for this internal flow, when it is transversely confined by compliant walls. Two distinct cases are considered, namely the case of two compliant walls with non-identical wall parameters and the case of identical compliant walls asymmetrically located about the fluid center line. The absolute instability characteristics are identified by following special saddle points (pinch points) of the dispersion relation in the complex wavenumber plane, and the flow’s stability properties are mapped out using parameter continuation techniques. The compliant walls introduce new modes which typically dominate the stability properties of the flow, in comparison to the case of pure shear layers. In the case of symmetrically located walls with non-identical wall parameters, it was found that the absolute stability properties are dominated by the modes linked to the more flexible of the two walls. In the case of identical walls asymmetrically confining the flow, it was found that these flows exhibit smaller regions of absolute instability in parameter space, when compared to the symmetric flow configuration.

A spatiotemporal stability analysis is conducted on a flow representing both jets and wakes, subject to confinement by identical compliant walls. The walls are placed at equal distances from the fluid center line for a range of wall and flow parameters. By following the position of special saddle points (pinch points) of the dispersion relation in the complex wave-number plane, the absolute and convective instability stability properties of the flow are determined for various system parameters. The compliant walls are shown to modify the shear-induced instabilities, which exist in the rigid wall case, as well as introduce new additional instabilities originating from the presence of the wall itself. It is observed that under certain system parameters, these wall-induced modes become the dominant instability present in the system and can induce an absolute instability into flows which are only convectively unstable when confined by rigid walls, as well as extending the region of absolute instability to large confinement parameters. Results are presented for both a piecewise linear velocity profile and a smooth velocity profile, with the results of the two studies in qualitative agreement.