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Center for Nonlinear Studies |
In this talk, I will describe my recent results on generation, propagation, interaction and dissipation modeling of internal waves and on the link between mixing processes in the ocean/ atmosphere and the internal wave field. The main goal of the talk is to present and discuss analytic and numeric models describing weakly-nonlinear and non-linear internal waves in the ocean and atmosphere. In particular, it will be shown that Lie Group Analysis provides rigorous derivation of exact solutions of non-linear modeling equations and that the previously known conservation laws can be recovered by means of this theory. Furthermore, utilization of Lie group analysis provides new conservation laws. Some of the invariant solutions, obtained by applying this theory, represent internal wave beams satisfying the energy radiation condition. Also, I plan to discuss a longitudinal atmospheric circulation model with the goal to illustrate the occurrence of solitary wave like solutions and splitting phenomenon for shallow water theory which has never been reported in previous studies.
Host: William Lipscomb