Nonlinear standing surface waves excited by an oscillating cylinder in a narrow rectangular cavity

Forced standing 2D surface waves in a narrow deep rectangular transparent cavity are studied experimentally and theoretically. Waves are excited by an oscillating fully submerged cylinder with a diameter small relative to the cavity’s length and axis normal to its long walls. The cylinder is forced to oscillate harmonically in the vertical direction with amplitudes smaller than its diameter at frequencies close to the resonant frequencies of the cavity. In experiments, the free surface motion is recorded by a video camera. The motion of the free surface's shape and the wave amplitude's dependence on the forcing amplitude and frequency is extracted from the sequence of video images. The surface motion is also simulated using the volume-of-fluid approach and independently, assuming irrotational flow with small dissipation. The experimental data agree with the results of both theoretical approaches and show that the effective resonance frequencies are downshifted from the cavity’s natural frequencies by a value proportional to the square of the cylinder diameter; the nonlinear effects cause further resonant frequency downshifting.