Y.K. Cheung

Instabilities and bifurcations of interfacial water waves

The fourth‐order Zakharov equation for interfacial waves of two‐layered fluids with finite depths is derived to include quintet interactions. Using this new equation the class I and class II instability and bifurcation of a two‐dimensional Stokes interfacial wave into a three‐dimensional steady wave is studied. Results are in good agreement with those by numerical calculations from the full unapproximated water wave and with experimental data.

Response in harbour due to incidence of second-order low-frequency waves

Abstract Using the method of multiple scales and matched asymptotic expansions, the response in a harbour due to the incidence of the set-down wave of a group wave train with narrow spectrum is investigated. The envelope of the incident wave train is assumed to modulate slowly in the direction of wave propagation. The relationship between the envelopes of incident waves and transmitted or scattered waves is derived. It is shown that the second-order scattered wave generated by the set-down wave of the incident wave train propagates only at the longwave celerity √ gh . This scattered wave in the harbour is discussed along with the response due to the set-down wave. The resonant response has been calculated for two types of geometries.