On Steady Vortex Flow in Two Dimensions. II.
Abstract
We extend the results of our previous work (Part I) 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 (in uniform translation). The existence of solutions and the asymptotic behavior of these solutions in a certain singular limit are established as in Part I 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 (in the appropriate function space); consequently, we find that there is nonexistence of solutions in some cases. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1982
- Accession Number
- ADA120966
Entities
People
- Bruce Turkington
Organizations
- University of Wisconsin–Madison