On the hysteresis phenomenon in the directly excited nonlinear resonant sloshing waves in a tank

Steady nonlinear resonant standing waves obtained in a rectangular tank by a direct excitation are studied in detail both experimentally and numerically. The experimental study demonstrates the existence of a well defined hysteresis between two quite different wave distributions in the tank. The dissipation coefficient at the wavemaker is estimated from the present experimental results. Numerical simulations based on the solution of the nonlinear Schrödinger equation, with the dissipation coefficient at the wavemaker obtained experimentally, show that this hysteresis may be reproduced in calculations when a nonlinear boundary condition at the wavemaker is adopted. Such a boundary condition is indeed supported by experimental evidence.