ON NONLINEAR BAROCLINIC WAVES AND ADJUSTMENT OF PANCAKE DYNAMICS

Three-dimensional nonhydrostatic Euler-Boussinesq equations are studie d for Bu = O(1) flows as well as in the asymptotic regime of strong st ratification and weak rotation. Reduced prognostic equations for ageos trophic components (divergent velocity potential and geostrophic depar ture/thermal wind imbalance) are analyzed. We describe classes of nonl inear anisotropic ageostrophic baroclinic waves which are generated by the strong nonlinear interactions between the quasi-geostrophic modes and inertio-gravity waves. In the asymptotic regime of strong stratif ication and weak rotation we show how switching on weak rotation trigg ers frontogenesis. The mechanism of the front formation is contraction in the horizontal dimension balanced by vertical shearing through cou pling of large horizontal and small vertical scales by weak rotation. Vertical slanting of these fronts is proportional to root mu where mu is the ratio of the Coriolis and Brunt-Vaisala parameters. These front s select slow baroclinic waves through nonlinear adjustment of the hor izontal scale to the vertical scale by weak rotation, and are the enve lope of inertio-gravity waves. Mathematically, this is generated by as ymptotic hyperbolic systems describing the strong nonlinear interactio ns between waves and potential vorticity dynamics. This frontogenesis yields vertical ''gluing'' of pancake dynamics, in contrast to the ind ependent dynamics of horizontal layers in strongly stratified turbulen ce without rotation.