Fluid•DTU seminar, Tuesday, Oct. 27, 2009, at 11:00, Bldg. 306 Aud. 34

The motivation for this work is that vortex equilibria are prevalent in a large class of physical settings that are characterized by different
mathematical models. A general and systematic approach for solving point vortex equilibria is presented.  We use the Hamiltonian point vortex model for the equations of motion. The problem is formulated as one in linear algebra with the positions of the vortices given, and singular value decomposition is used to determine the vortex strengths necessary for relative equilibrium. We demonstrate that this approach provides a good model for various types of vortex lattices, and illustrate its usefulness with two applications.

 

(1) Recent experiments on the formation of vortex lattices in Bose-Einstein condensates has produced the need for a mathematical theory that is capable of predicting a broader class of lattice patterns, ones that are free of discrete-symmetries and can form in a random environment.  We describe how the linear algebra approach can be used in conjunction with a Brownian ratchet scheme to identify asymmetric equilibria.

 

(2) We show how this approach can be used to study fluid transport in idealized geophysical flows. Specifically, we present a method of identifying the full family of streamline topologies and bifurcations for vortex streets on the sphere in the co-rotating frame.