The ocean contains an enormous amount of energy. That power can be creative, through wave-energy extractors, or destructive, such as a tsunami taking hundreds of thousands of lives. We seek to understand how to harness and control this power. In this pursuit, we investigate how shear currents from below affect the surface up above. Historically, this task has been dealt with by restricting to the case of shear currents with constant vorticity. This thesis expands these ideas to non-constant vorticity through a technique called Whitham averaging. This process leaves us with a system of four partial differential equations which we solve numerically, via the Finite-Volume Method, to model the ocean’s surface. Finally, we use this model to investigate the effect of vorticity on the surface.
