The spontaneous oscillations of a circular hydraulic jump

The circular hydraulic jump is a frequently observed phenomenon occuring when a vertical jet of liquid impinges on a horizontal surface. Most of the work found in the literature focuses on the stationary states of the circular hydraulic jump by for example trying to predict its radius. In our study, 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 waves eigenmodes. (ArXiv: https://arxiv.org/abs/2302.06193)