Numerical and Experimental Study of the Interaction of AN Internal Solitary Wave with a Slope-Shelf Topography
The complete Navier-Stokes and diffusion equations are used to study real fluid effects on generation, propagation, and shoaling of an internal solitary wave on the pycnocline of a two-layered fluid. The equations are solved by a numerical scheme that eliminates the truncation errors that would mask real fluid effects at high Reynolds numbers. The scheme is verified by known theoretical and laboratory results. Mass transport due to the passage of an internal solitary wave was calculated. The model is used to study the "weak" interaction of the soliton with a slope-shelf. For the purpose of this study the interaction is said to be "weak" if no breaking occurs in the interaction. It is found that the scattering of the incoming soliton into one or more solitons of reversed polarity is always possible if (h_2 -h_1) changes sign as the soliton shoals on the slope (h_1 and h _2 are the depth of the upper and lower layers respectively). The mechanism involves the building up of mass and potential energy in the fluid at the back of the wave when its forward motion is impeded by the slope. The build-up subsequently collapses and solitons consistent with the fluid depths on the shelf emerge. The results of a new laboratory experiment are presented for comparison. If the sign of h_2-h_1 remains unchanged during the shoaling process, the reversal of polarity does not occur. But the mechanisms are however still similar. When the dimensionless amplitude ratio was sufficiently large, breaking occurred near the shelf-edge. The interaction is said to be "strong" when wave-breaking occurs. It was found that for steep slopes (slopes larger than 1:8) breaking was of the overturning type and for mild slopes only shear instability occurred. An approximate set of curves for different slopes in the dimensionless amplitude vs. Reynolds number plane are presented, separating regions with breaking from regions without breaking. Energy dissipation and particle trajectories due to the interaction process are also given.
- Pub Date:
- SOLITARY WAVE;
- Engineering: Civil; Physics: Fluid and Plasma