Over-reflection in lab: the all-sufficient cause of instability of an annular supersonic shear in simulations on free-surface shallow water

Abstract

Presented are results of the pioneering research on the over-reflection instability of an annular ‘supersonic’ shear in experiments on free-surface shallow water covering a differentially rotating and properly shaped bottom (characteristic waves on shallow water play the role of sound, all alternative shear instabilities are suppressed due to specificity of the rotation profile and experimental procedure). The consideration focuses upon distinctive features of the structures generated by the instability as perturbations of shallow-water thickness. The features of the structures observed are compared with those predicted by an original theory. The structures are also readily interpreted as a superposition of Huygens-Mach fronts that are multiply over-reflected from the shear, having been induced by a supersonic disturbance moving along it. Owing to the annular geometry, the instability in the experiments develops even in absence of external boundaries that are universally included in traditional theoretical schemes for feedback necessary for the wave generation.