WAVE PATTERNS IN A STREAM AT NEAR-CRITICAL SPEED
Abstract
The two-dimensional free-surface flow generated by a singularity moving with near-critical speed (i.e. with Froude number referred to the water depth near unity) is solved by using the method of matched asymptotic expansions. In the vicinity of the singularity the problem is solved by an infinitesimal wave expansion (inner expansion) while at large distances from the singularity shallow water theory provides the proper solution (outer expansion). A composite expansion provides a uniformly-valid solution for the velocity components, the free-surface profile and the drag force. These two basic approaches of water-wave theory are shown to be solutions of the same flow problem, but valid in different regions. Although the inner expansion satisfies linear equations, the solution depends nonlinearly on the small parameter of the problem (the singularity strength).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1968
- Accession Number
- AD0665690
Entities
People
- G. Dagan