Lagrangian approach to geostrophic adjustment of frontal anomalies in a stratified fluid

Geostrophic adjustment of frontal anomalies in a rotating continuously stratified fluid is studied in the standard framework of strictly rectilinear fronts and jets. Lagrangian approach to this problem is developed allowing to analyze. in a conceptually and technically simple way. both major problems or the nonlinear adjustment: the existence or a smooth adjusted state for a given set or initial conditions and the attainability of the adjusted state during the adjustment process. Dynamical splitting into balanced (adjusted state) and unbalanced (inertia-gravity waves) motions becomes transparent in the Lagrangian approach. Conditions of existence or the balanced state in the unbalanced domain are established. It is shown that nonexistence or a smooth adjusted state in the vertically bounded domains is generic and a parallel with file classical scenario or deformation frontogenesis is developed. Small perturbations around smooth adjusted states are then studied with special emphasis on the wave-trapping inside the jet, front. Trapped modes with horizontal scales comparable to the width of the jet are explicitly constructed for a barotropic jet and their evolution is studied with the help or the WKB-approximation for weakly baroclinic jets. Modifications or the standard scenario of adjustment due to subinertial (quasi-) trapped modes and implications for data analysis are discussed.