Hamiltonian contour dynamics and applications

POSTER

Abstract

It is known that contour dynamics (CD) can be viewed as a Hamiltonian system defined on a phase space of parameterization invariant functionals of closed curves [1-3]. This structure can be shown to follow from a general theory that reduces to both the noncanonical Hamiltonian structure of the two-dimensional Euler equations and CD. Generalizations to 2D and 3D quasigeostrophic systems also fit this general theory. This opens the way to use tools from Hamiltonian dynamics to interpret CD results. We will explore generalizations of the Kirchhoff vortex dynamics as integrable and non-integrable Hamiltonian systems, and Hamiltonian bifurcations. In addition, perturbation theory in terms of amplitude expansions for single and multi-contours will be discussed in several contexts including two contour barotropic instability and interactions between baroclinic and barotropic waves on a barotropic vortex.

[1] Bell, G.I., The nonlinear evolution of a perturbed axisymmetric eddy; in GFD Summer Program, 1990, pp. 232–249.

[2] Morrison, P.J. and Flierl, G.R., Hamiltonian Contour Dynamics. Bull. Amer. Phys. Soc., 2001, 46, ED4.

[3] Morrison, P.J., Hamiltonian and Action Principle Formulations of Plasma Physics. Phys. Plasmas, 2005, 12,

058102.

Presenters

  • Philip J Morrison

    Department of Physics and Institute for Fusion Studies, University of Texas at Austin, 78712 USA, Physcis Department, University of Texas at Austin, Austin, TX, University of Texas at Austin

Authors

  • Philip J Morrison

    Department of Physics and Institute for Fusion Studies, University of Texas at Austin, 78712 USA, Physcis Department, University of Texas at Austin, Austin, TX, University of Texas at Austin

  • Glenn R Flierl

    Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA