Numerical investigation of internal solitary waves of elevation type propagating on a uniform slope

Abstract

Numerous laboratory-scale physical experiments and numerical simulations have been carried out to explore the shoaling dynamics of internal solitary waves (ISWs) on slope topographies. Detailed features during wave breaking have been investigated under relatively low Reynolds numbers, but for real ocean-scale or lake-scale scenarios with a much higher Reynolds number, laboratory-scale modeling is inadequate to capture the three-dimensional turbulent characteristics in the wave shoaling process. As a result, a three-dimensional large-eddy simulation (LES) is performed in the present study to investigate the shoaling process of the elevation-typed ISWs traveling on uniform slopes in a two-layer fluid system. Scale effects due to the Reynolds numbers (varied from 103 to 105) and three-dimensional characteristics during wave shoaling are also explored and discussed. Detailed ISW-slope interaction dynamics, including the typical shoaling features, the characteristics of internal boluses, and both the velocity field and the energy transformation, are systematically obtained and analyzed. It is found that, while reaching the maximum vertical displacement (i.e., maximum run-up height), the frontal part of the heavier lower-layer fluid can evolve into the internal bolus if the internal Iribarren number, Ir, defined as the ratio of the topographic slope and the square root of the incident wave steepness, is less than 0.65. The maximum wave-induced velocities and energy loss are also well related to Ir. Empirical regressed equations for seven important physical parameters during the shoaling process are also proposed. The extreme velocities, wave energy loss, and three-dimensionality of the flow field are all identified to be very sensitive to Reynolds numbers, indicating that traditional two-dimensional laboratory-scale modeling tools may be insufficient to accurately capture the shoaling mechanisms of the ISWs of elevation type.