Water entry of spheres into a rotating liquid

TL;DR

This study investigates how the rotation of a liquid pool influences the water entry dynamics of spheres, revealing effects on cavity transition, pressure fields, and pinch-off times through experiments, simulations, and theory.

Contribution

It uncovers the role of pool rotation and the rotational number in cavity evolution, advancing understanding of water entry phenomena in rotating fluids.

Findings

Rotation advances cavity transition from deep to surface seal.

Rotating liquid increases underwater pressure and reduces cavity neck airflow.

Pinch-off time follows a 1/2 power-law with Froude number, with rotation reducing the prefactor.

Abstract

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 $\mathcal{S} \equiv \omega R_0/U_0$ on the transient cavity dynamics is unveiled, where $R_0$ is the sphere radius, $\omega$ the angular speed of the liquid, and $U_0$ 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 $\omega$. 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.