Experimental and theoretical investigation of nonlinear sloshing waves in a rectangular channel

Experimental and theoretical studies of sloshing waves in a rectangular channel in the vicinity of the second cutoff frequency are presented. The experiments were performed in a wave tank which is 1. 2m wide, 18m long and 0. 9m deep. Sloshing waves were generated by a computer-controlled segmented wavemaker consisting of four independent modules. A sharp transition between two wave patterns, which exhibited hysteresis-type behaviour, was observed. At lower forcing frequencies a steady wave regime was obtained, while at higher frequencies modulation on a long timescale appeared. At stronger forcing, solitons were generated periodically at the wavemaker and then propagated away with a seemingly constant velocity. Experimental results are compared with numerical solutions of the appropriate nonlinear Schrodinger equation, a derivation of which is also presented. The importance of dissipation on the physical processes of wave evolution is discussed, and a simple dissipative model is suggested and incorporated in the governing equations.