On the Swirling Flow between Rotating Coaxial Disks, Asymptotic Behavior II.
Abstract
Consider solutions (H(x,epsilon),G(x,epsilon)) of the von Karman equations for the swirling flow between two rotating coaxial disks epsilon H(superscript(iv)) + HH''' + GG' = 0, and epsilon G'' + HG' - H'G = 0. We assume that abs. val. (H(x, epsilon)) + abs. val. (H'(x, epsilon)) + abs. val. G(x, epsilon)) < or = B. This work considers shapes and asymptotic behavior as epsilon approaches 0+. We consider the type of limit functions (ave. H(x), ave. G(x)) that are permissible. In particular, if (H(x, epsilon),G(x, epsilon)) also satisfy the boundary conditions H(0, epsilon) = H(1, epsilon) = 0, H'(0, epsilon) = H'(1, epsilon) = 0 then ave. H(x) has no simple zeros. That is, there does not exist a point z an element of (0, 1) such that ave. H(z) = 0, ave. H'(z) is not equal to 0. Moreover, the case of 'cells' which oscillate is studied in detail. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA077126
Entities
People
- Heinz Otto Kreiss
- Seymour V. Parter
Organizations
- University of Wisconsin–Madison