Internal Solitary Wave Tunnelling

B.R. Sutherland, S. Keating and I. Shrivastava

J. Fluid Mech.,

We report upon laboratory experiments and numerical simulations examining the evolution of an interfacial internal solitary wave incident upon a triangular ridge whose peak lies below the interface. If the ridge is moderately large, the wave is observed to shoal and break similar to solitary waves shoaling upon a constant slope, but interfacial waves are also observed to transmit over and reflect from the ridge. In laboratory experiments, by measuring the interface displacement as it evolves in time, we measure the relative transmission, reflection and deposition of available potential energy after the incident wave has interacted with the ridge. The numerical simulations of lab-scale and oceanic-scale waves measure both the available potential and kinetic energy to determine the partition of incident energy into that which is transmitted, reflected and deposited. From shallow water theory, we define a critical amplitude, Ac, above which interfacial waves are unstable. The transmission is found to decrease from one to zero as the ratio of the incident wave amplitude to Ac increases from less than to greater than one. Empirical fits are made to analytic curves through measurements of the transmission and reflection coefficients.