A note on liquid vortex sloshing and Kelvin's equilibria

Abstract

Observations of liquid vortex sloshing and Kelvin's equilibrium states were made inside a cylindrical container using a spinning disk near its base. Both steady and periodic free-surface sloshing phenomena were found to take place. During periodic sloshing, the air core sustained shape transformations, assuming an elliptical cross-section at the end, and then collapsed forming a pair of vortices. Kelvin's equilibrium states emerged at lower liquid levels. These were stable within an interval of rotational speeds. The bandwidth of stationary states decreased as the wavenumber (N) increased. For N greater than six, the states appeared critically stable. Between equilibria, unstable transitional regions were found to exist. As the liquid level was decreased, the core shape spectrum shifted towards smaller frequencies.