Oscillations of an unstable mixing layer impinging upon an edge

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Abstract
The central features of lihear and nonlinear disturbance growth in the unstable shear layer, mechanisms of impingement of the resultant vortices on the edge, induced force on the wedge, and upstream influence in the form of induced velocity fluctuations at separation are examined by simultaneous visualization, velocity, and force-measurement techniques.The nature of the vortex–wedge interaction, and the associated force on the wedge, are directly related to the induced velocity at the upstream separation edge, thereby providing the essential ‘feedback’ for the self-sustained oscillation. Velocity fluctuations at the upper and lower sides of the separation edge tend to be π out of phase, a condition that is maintained along the outer boundaries of the downstream shear layer. Moreover, the phase between velocity fluctuations at separation and impingement satisfies the relation 2nπ, where n is an integer.The shear layer downstream of the separation edge initially forms an asymmetric wake, which evolves into large-scale vortices, all of which have a circulation appropriate to the high-speed side. The disturbance amplification associated with the high-speed side dominates from the separation edge onwards, precluding development of instabilities associated with the low-speed side.Regardless of the initial amplitude of the disturbance induced at the separation edge, the same saturation amplitude is attained in the downstream (nonlinear) region of the shear layer, underscoring the fact that variations in force amplitude at the wedge are dominated by the type of vortex–edge interaction mechanism. The sensitivity of this interaction to small offsets between the vortex centre and the leading edge entails that jumps in frequency of oscillation are also associated with jumps in the force amplitude.

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