Instabilities in Fluids: Linear and Non-linear Analysis of Waves and Patterns in the Environment

This course describes natural patterns arising from instabilities in nature, and discusses their importance in the environment. We will analyze phenomena at various scales, as diverse as wave breaking at the ocean surface, internal mixing in the atmosphere and the ocean, volcanic plumes, convection cells in the atmosphere, the break-up of fluid ligaments or bubble bursting at an interface. The course will detail mathematical tools (linear and non-linear stability analysis, symmetry arguments, solutions to non-linear equations such as shocks and solitons), as well as present laboratory and numerical demonstrations of the instabilities.