Evolution of harmonic interfacial wave pattern over a bottom layer by surface wave

Resonant wave interaction is responsible for various marine and coastal phenomena. Of particular importance are mechanisms accounting for mixing of bottom turbid layer at intermediate and shallow water depths. Recent field data indicates growth of harmonic interfacial modes at the interface between turbid layer and clear water by a wave train on the free surface. In this paper, we propose a particular surface-interfacial resonant wave interaction as the responsible mechanism and study it theoretically and experimentally. We show that four oblique harmonic interfacial waves forming a quasi-standing wave in a wave flume may start growing from background noise level through a cubic resonant wave interaction with a surface wave. The competing effects of viscous decaying, surface wave triggering, and nonlinear modulation eventually lead to a stabilized interfacial wave motion. A third-order resonant interaction analysis shows that the interfacial waves exhibit greater growth potential when their propagation directions deviate from that of the surface wave. A set of carefully conducted experiments is used to support the theoretical predictions. The experimental observations also indicate that there exists a frequency range for which harmonic interfacial waves grow while other forms of interfacial instability are absent.