Yangxin He, Applied Mathematics, University of Waterloo
Internal waves on the continental shelf: interactions with along shelf currents and shoaling solitary waves
We propose two separate projects: the shoaling of a single internal solitary wave (ISW) over piecewise bathymetry and the effect of an along shelf current on internal waves generated by tide-topography interactions at the continental shelf/slope.
The bathymetry we have used so far in the shoaling ISWs model is a simple uniform slope. We propose to examine a two-slope topography based on the previous research. We will start with a simple two-layer pycnocline stratification with weakly stratified layers above and below the pycnocline and move on with more complicated density profiles later. The focus of this project is to determine the wave breaking location.
The project of the interactions of IWs with a geostrophic current is motivated by data from the Gulf Stream, where enhanced IW activity near the ocean side of the Gulf Stream is observed. We propose to begin the investigation by constructing a simple two-dimensional model with a flat bottom. The model is initialized with a geostrophic current balanced by a horizontally varying stratification. Internal waves, driven at a lateral boundary, will propagate in a direction perpendicular to the current and the resulting interaction will be studied. Stratifications and currents used will be based on observations from the Gulf Stream.
We will discuss the parameters that need to be varied and my future research plans.