On steady vortex flow in two dimensions, 2
Abstract
We extend the results of our previous work concerning steady ideal flow with vorticity in a bounded domain to the situation where the domain is unbounded and the flow is uniform at infinity. Prototypical examples include vortex pairs and Foppl vortex wakes behind a cylinder. The existence of solutions and the asymptotic behavior of these solutions in a certain singular limit are established as in part 1 using a direct variational method. The variational principle needed here is rather nonstandard, and so a detailed discussion of its formulation is given. Special difficulties arise for flows in an unbounded domain due to a lack of compactness; consequently, we find that there is nonexistence of solutions in some cases.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 July 1982
 Bibcode:
 1982wisc.reptR....T
 Keywords:

 Boundary Value Problems;
 Steady Flow;
 Vortices;
 Asymptotic Methods;
 Constraints;
 Variational Principles;
 Wakes;
 Fluid Mechanics and Heat Transfer