Nonlinear instability of wavy shear flow

This thesis is concerned with the mathematical description of stadium-sized rolls that form in the upper ocean. The rolls result from the interaction of surface waves with an ocean current. Known as Langmuir circulation, the rolls help to mix the ocean and form a layer about 100m deep. Since this layer stores an enormous amount of heat that affects weather and climate, of key interest is to understand the evolution of Langmuir circulation and the role they play in the layer’s formation. This thesis is thus a systematic study of Langmuir circulation and the instability that gives rise to them.