Oscillations and cavity modes in the circular hydraulic jump

TL;DR

This paper investigates the spontaneous oscillations of circular hydraulic jumps caused by water jet impacts, revealing that oscillation frequency aligns with surface wave eigenmodes of the cavity, indicating a self-induced interaction.

Contribution

It demonstrates that jump oscillations are driven by surface wave eigenmodes, linking fluid dynamics with cavity wave theory in a novel way.

Findings

Oscillation period is independent of flow rate.

Oscillation period varies linearly with disk radius.

Jump oscillations match surface wave eigenfrequencies.

Abstract

We report spontaneous oscillations of circular hydraulic jumps created by the impact of a submillimeter water jet on a solid disk. The jet flow rate is shown to condition the occurrence of the oscillations while their period is independent of this parameter. The period, however, varies linearly with the disk radius. This dependency is rationalized by investigating surface gravity wave modes in the cavity formed by the disk. We show that the jump oscillation frequency systematically matches one of the surface wave disk-cavity eigenfrequencies, leading to the conclusion that the oscillations are self-induced by the interaction between the jump and surface wave eigenmodes.