Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank

Experiments are described on surface gravity-capillary waves in a 70 cm × 2.8 cm rectangular tank undergoing small vertical oscillations. The large aspect ratio of the tank permits study of several neighbouring two-dimensional wave modes; their onset, hysteresis and instability. Two water depths, close to one and two centimetres, are investigated in detail. Thresholds are determined for wave onset from a flat surface and the hysteretic return to a flat surface from finite-amplitude waves. Also, conditions at which a pure standing wave becomes unstable to other modes are established. Our finding of hysteresis below the minimum forcing for linear wave-onset suggests that nonlinear forcing and nonlinear damping are both significant, as recently suggested by Miles ( J. Fluid Mechanics 248 (1993) 671 ) A theoretical model, incorporating these effects, is analysed and the corresponding hysteresis boundaries established. These are broadly consistent with our experimental results.