Nonlinear resonance in barotropic-baroclinic transfer generated by bottom sills

Internal waves generated by surface perturbations are studied in a two-layer fluid in the presence of two thin sills of equal height in the lower layer, both experimentally and numerically. Small amplitude surface waves are found to generate internal waves of large amplitude at the density interface in between the two sills. The largest amplitude internal waves appear if a resonance condition is fulfilled: if half of the wavelength of the internal wave of the period of the external perturbation fits into the distance between the two sills in the form of standing waves. The internal waves are then apparently nonlinear, nevertheless, the predictions of a linear theory for the resonance condition apply by taking into account a systematic change in the wavelength caused by nonlinearity, and the deviation from a sharp density interface. Interestingly, the shape of these internal waves is found to be nearly sinusoidal. A precise classification proves them to be cnoidal waves with a small elliptic parameter m.