Abstract
The purpose of this introductory session is to describe the basic phenomenology of rapidly rotating incompressible fluids and to provide an introduction to the mathematical formalism.
Under the combined effect of internal pressure and uniform rotation, an incompressible fluid exhibits a two-dimensional structure, behaving essentially like a solid in the direction parallel to the axis of rotation (Taylor-Proudman columns). Fluctuations around this equilibrium, known as the geostrophic state, are described by waves called Poincaré waves.
The propagation of these waves is governed by nonlocal pseudodifferential operators. We will show how classical methods of wave analysis, based on Fourier analysis, can be extended to these situations, and will discuss in particular the concepts of dispersion relations, phase velocity, group velocity, and the dispersive properties of Poincaré waves.
