The ocean and lakes are stratified due to salinity and temperature. The fundamental mode of internal waves associated with stratification induces a large current over the lake bottom when the bottom is sloping. When the internal waves shoal, they lose their energy to turbulence because of mixing due to internal wave breaking. The mixing may be associated with sediment resuspension and lead to transport of the resuspended sediment. In this study, we focused on mass transportation caused by internal waves shoaling on a slope in a two-layer system and the study was carried out using three methods; (1) theoretical analysis based on the Boussinesq-type equations; (2) laboratory experiment; (3) numerical computation.
The theoretical part provides the Boussinesq-type equations for a two-layer system that was solved under perfect reflection. The solution of the Boussinesq-type equations was divided into two solutions: the solution due to the steepening process; and the solution due to the dispersion process, to clarify the mechanism of the vertical convection. The solution due to the steepening process was obtained by using the method by Carrier and Greenspan (1958, JFM Vol.4) and the solution due to the dispersion process was numerically obtained. It was possible to obtain the residual current by averaging the flow field for one period of internal waves because the intrusion occurs around the interface and the anti-clockwise circulation appears adjacent to the sloping bottom. From the instability analysis, the critical amplitude of internal waves, CS, was derived and CS was demonstrated to be a function of the number of internal waves over a slope, BP.
Laboratory experiment was carried out to clarify the mechanism underlying the mixing effect because the theoretical analysis can only provide the solution for perfect reflection. To determine the energy loss, the reflection coefficient was evaluated from the internal wave gauges data. This showed that the reflection coefficient is modeled by the normalized amplitude of incident internal waves by CS. The residual current was measured via the Portable Flux Profiler, PFP, which is a laser Doppler current meter. In contrast to the residual current obtained from the theoretical analysis with perfect reflection, the residual current obtained from experiment showed that clockwise circulation occurs adjacent to the sloping bottom and intrusion appears beneath the interface.
In order to determine more detailed information for the case when internal wave breaking occurs on a slope, the numerical computation was preceded by MEL3D, involving non-hydrostatic, three dimensional and large eddy simulation model. From these results, it was shown that dissipation has a major role in the loss of kinetic energy and it is found that there are three main types of flow in the residual current: on-slope current above the interface; clockwise circulation around the interface adjacent to the slope; anti-clockwise circulation beneath the interface, when internal waves break on a sloping bottom. |
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