Water Waves Generated by a Slowly Moving Two-Dimensional Body. Part 1.
Abstract
Low-speed motion of a ship leads to a singular perturbation problem as speed approaches zero, since waves occur only in a boundary layers of vanishing thickness at the free surface. The complete solution consists of the singular expansion superposed on a regular expansion. The latter (the naive expansion ) by itself satisfies all conditions in the lower half-space below the undisturbed free surface, but it does not represent the boundary layer. For the case of a two-dimensional surface-piercing body, it is shown that the regular perturbation series fails to satisfy the body boundary condition in a small wetted region just above the level of the undisturbed free surface. This fact leads to a nonhomogeneous body boundary condition that must be satisfied by the singular expansion. Without such a condition, the singular part of the solution (which represents the real wave motion) would satisfy purely homogeneous conditions and thus would be indeterminate. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1982
- Accession Number
- ADA131909
Entities
People
- Si-xiong Chen
- T. Francis Ogilvie
Organizations
- University of Michigan