Date of Award
Master of Science (MS)
Hetons are defined, in two-layer quasigeostrophy, as tilted counter-rotating baroclinic vortex pairs with each vortex present in a different layer. The study of hetons is motivated by their usage within the context of two-layer quasigeostrophic theory to model the transport of heat in a number of geophysical flows including, perhaps most famously, advection in the open ocean. A number of variations and generalizations of the heton concept exist in literature. Here, following the work of V.M. Gryanik, we investigate the three-dimensional point vortex heton. We start with the derivation of a non-canonical Hamiltonian system of 2n ODEs corresponding to point vortex solutions of the Quasigeostrophic Potential Vorticity Equation in an unbounded three-dimensional domain, where n is the number of point vortices. We then show that three-dimensional hetons arise naturally as solutions of this system when n = 2. The dynamics of a single three-dimensional heton in a comoving frame are then discussed. Fixed points and bifurcations in the Lagrangian trajectories are then catalogued using various analytical and numerical techniques, and finally, the volume trapped by a single three-dimensional heton is calculated numerically for various values of the parameter Z – corresponding to the vertical distance between the counter-rotating vortices that compose the heton.
Sivakumar, Adhithiya, "The Dynamics of a Three-Dimensional Heton" (2019). Applied Mathematics Graduate Theses & Dissertations. 146.