Multi-mode resonances in fluids

When a lightly damped fluid resonator is forced near its fundamental frequency, the most usual response is one in which the fluid oscillates in the corresponding eigenmode with an amplitude response similar to that of a Duffing oscillator. Examples are the sloshing of a horizontally oscillated tank or acoustic oscillations in a resonator of general shape. However, multiple eigenmodes can be excited if the spectrum is either commensurate or degenerate and both acoustic resonance and the sloshing of shallow water in a nearly square container exemplify both these exceptional cases. In this paper we investigate how the response of such systems depends on geometry and dispersion.