Water entry of spheres into a rotating liquid

The transient cavity dynamics during water entry of a heavy, non-rotating sphere impacting a rotating pool of liquid is studied experimentally, numerically and theoretically. We show that the pool rotation advances the transition of the cavity type – from deep seal to surface seal – marked by a reduction in the transitional Froude number. The role of the dimensionless rotational number S ≡ ωR0/U0 on the transient cavity dynamics is unveiled, where R0 is the sphere radius, ω the angular speed of the liquid and U0 the impact velocity. The rotating background liquid has two discernible effects on the cavity evolution. Firstly, an increase in the underwater pressure field due to centripetal effects; and secondly, a reduction in the pressure of airflow in the cavity neck near the water surface. The non-dimensional pinch-off time of the deep seal shows a robust 1/2 power-law dependence on the Froude number, but with a reducing prefactor for increasing ω. Our findings reveal that the effects of a rotating background liquid on the water entry can be traced back to the subtle differences in the initial stage splash and the near-surface cavity dynamics