Rossby wave equations characterize a class of wave phenomena occurring in geophysical fluid dynamics. One technique useful in the analysis of these waves is the geometrical optics, or multi-dimensional WKB technique. Near caustics, e.g., in critical regions, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to study Rossby waves near caustics.
The linearized vorticity equation serves to model a number of wave phenomena in geophysical fluid dynamics. One technique that has been applied to this equation is the geometrical optics, or multi-dimensional WKB technique. Near caustics, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to determine an asymptotic solution of the linearized vorticity equation and to study associated wave...
We first introduce the notion of microdifferential operators of WKB type and then develop their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB solution for such an operator is given through the symbol calculus of microdifferential operators, and their local structure near their turning points is discussed by a Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book equation is given in Appendix.