Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

An adaptive asymptotic nonlinear modal system is used for systematic quantification of three-dimensional steady-state resonant sloshing in a square base tank with a finite fill depth. The depth/breadth ratios are ⩾0.4. The tank is laterally excited with frequency close to the lowest natural frequency. The main emphasis is on the “swirling” wave regime and its special features, e.g., stability, feedback of higher modes, and regular and irregular switch of the apparent direction of rotation. Theoretical results are validated for both steady-state solutions and “beating” that does not die out in experimental investigations. Frequency domains with no stable steady-state waves and occurrence of “chaotic” waves are discussed.