Role of the Boundary Conditions in the Problem of the Linear Stability of the Sedov Point Blast Solution.
Abstract
The linear stability of those Sedov blast wave similarity solutions for which the flow is homologous behind the shock, of which the best-known example is the Primakoff point blast model, along with that of their two-dimensional counterparts, has previously been demonstrated analytically by Bernstein and Book (1980). Their conclusion that the eigenmodes are stable applies to all perturbations in the three-dimensional case, and to all flutelike (k sub z = 0) modes in the two-dimensional case. Gaffet (1984) has argued that the treatment did not allow for a jump in the entropy of the perturbations at the shock front, and so must be incorrect. The analysis of Bernstein and Book, however, can easily be extended to include anisentropic perturbations. The additional terms, which have the same time dependence as the basic state, and therefore cannot give rise to instability, in any case drop out of the treatment. The resulting eigenvalued problem is identical with solved by Bernstein and Book, whose conclusion that the Primakoff-Sedov blast waves are stable is therefore restored.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 16, 1986
- Accession Number
- ADA168080
Entities
People
- D. L. Book
Organizations
- United States Naval Research Laboratory