Beyond Two-Dimensional Turbulence in GFD

The former chapter dealt with strictly two-dimensional turbulence, which is a sort of zero-order approximation for the dynamics of large-scale flows in Geophysical Fluid Dynamics (GFD). In fact these motions, although in thin layers, are strongly influenced by stratification effects which are threedimensional. A first step in this study is the quasi geostrophic theory, allowing one to write quasi two-dimensional evolution equations for the large scales of a stably-stratified shallow flow on a rapidly-rotating sphere. We will see how the two-dimensional dynamics is modified by quasi geostrophy. We will also try to explain the main mechanisms of baroclinic instability, resulting from the existence of horizontal thermal fronts, which is at the origin of storms in the atmosphere. This will necessitate to look at non-geostrophic effects. We will give a version of quasi geostrophic theory in a fluid with N layers of different density which is currently used for ocean-circulation modelling. We will study the interaction of geostrophic layers with Ekman layers close to boundaries. At a smaller scale, we will provide a model of tornado generation in the atmospheric boundary layer in the presence of localized thermal convection. We will also present a description of waves such as Rossby waves. We will discuss Jupiter external atmosphere made of alternate zonal jets. Finally the statistical concept of geostrophic turbulence will be discussed.