Chebyshev polynomials

In this thesis, a 2D CHebyshev spectral domain decomposition method is developed for simulating the generation and propagation of internal waves over a topography. While the problem of stratified flow over topography is by no means a new one, many aspects of internal wave generation and breaking are still poorly understood. This thesis aims to reproduce certain observed features of internal waves by using a Chebyshev collation method in both spatial directions. The numerical model solves the inviscid, incomprehensible, fully non-linear, non-hydrostatic Boussinesq equations in the vorticity-streamfunction formulation. A number of important features of internal waves over topography are captured with the present model, including the onset of wave-breaking at sub-critical Froude numbers, up to the point of overturning of the pycnoclines. Density contours and wave spectra are presented for different combinations of Froude numbers, stratifications and topographic slope.