Harmonic generation of interfacial waves at a submerged bathymetric ridge

Abstract

[1] When two-layer, periodic, interfacial wave trains pass over a Gaussian ridge, waves of higher harmonic frequency can be excited at the ridge, which then propagate downstream independently of the incident wave. In laboratory experiments, the amount of energy transferred to higher harmonic frequencies increases with the nonlinearity of the main wave over the ridge crest. When the wave nonlinearity is increased to the point where breaking occurs over the ridge, harmonic generation can still occur. The length scale of the obstacle relative to the wavelength can also influence the energy transfer, which is consistent with analogous surface wave studies. The upper limit for which harmonic frequencies can be excited is set by the stratification. This wave-topography interaction provides a possible mechanism for transferring energy in the internal wavefield to smaller scales.

The mixing efficiency of interfacial waves breaking at a ridge: 1. Overall mixing efficiency

“…Once waves begin to break, the total incident wave energy transmitted past the ridge decreases from about 60 to 30% and an increasing portion is dissipated in the breaking event. As discussed by Hult et al [2010], waves of higher harmonic frequencies can be excited when a train of periodic waves passes over the ridge and thus the transmitted wave energy at twice the forcing frequency (2 ω 1 ) is shown separately from the rest of the transmitted wave energy. The energy transmitted at twice the forcing frequency (2 ω 1 ) peaks when a ∞ / h r ≈ 0.4.…”

“…As seen in Figure 8a, the amount of energy reflected from the ridge tends to increase with the incident wavelength, whereas viscous decay tends to damp shorter waves more quickly. The wave nonlinearity, the strength of the stratification relative to the wave frequency, and the wavelength relative to the topographic length can affect the excitement of higher harmonics [ Hult et al , 2010].…”