Resonant sloshing in circular cylinders : counter-rotating waves and triadic interactions
Liquid sloshing ---the dynamics of a liquid free surface induced by the motion of its container--- plays a key role in many industrial and engineering applications, ranging from cell growth in bioreactors to ship tanker design. In this talk, we present a weakly nonlinear analysis (WNL) that yields a system of amplitude equations describing the resonant responses of dominant harmonic modes to time-periodic elliptic container orbits within circular cylinders.
We first examine the influence of the ratio between the minor and major axes of the forcing orbit, revealing a wide range of wave regimes, including planar waves, irregular dynamics, and swirling waves. In particular, we experimentally demonstrate the existence of stable counter-directed waves, as can be anticipated by WNL analysis.
In a second part, we focus on the role of the fluid depth. By selecting a depth that allows three-wave resonant interactions, we observe the growth of daughter waves driven by nonlinear energy transfer from the primary mode excited by the forcing. In this regime, the WNL framework enables quantitative predictions of both the saturated wave amplitudes and the transient dynamics.
Contact Nathanaël Machicoane for more information or to schedule a discussion with the seminar speaker.