SINGULAR PERTURBATION PROBLEMS IN SHIP HYDRODYNAMICS

The paper is a survey of a group of ship hydrodynamics problems that have certain solution methods in common. The problems are all formulated as perturbation problems, that is, the phenomena under study involve small disturbances from a basic state that can be described adequately without any special difficulties. The methods of solution make explicit use of the fact that the disturbances of the basic state are small. Mathematically, this is formalized by the introduction of one or more small parameters which serve as measures of the smallness of various quantities. The solutions obtained will generally be more nearly valid for small values of the parameter. Special techniques are needed for treating such problems, and we have two which are especially valuable: 1) The Method of Matched Asymptotic Expansions, and 2) The Method of Multiple-Scale Expansions. The two methods emphasized in this paper can also be applied to problems involving an infinite fluid. In fact, neither method was applied specifically to free-surface problems until quite recent times. Section 2 of this paper is devoted to several infinite-fluid problems. The justification is almost entirely on didactic grounds. The methods can be made much clearer in these simpler problems, and so are included here, although in some cases the infinite-fluid problems can be treated adequately by more elementary methods. Most of the material in this paper has appeared in print elsewhere. The intention has been to present a coherent account of the treatment of singular perturbation problems in ship hydrodynamics, and so solutions by other people have been reworked and put into a common notation and a common format. In some cases, conscious decisions to follow certain routes and to ignore others have been made.

  • Corporate Authors:

    University of Michigan, Ann Arbor

    Department of Naval Architects and Marine Engineers
    Ann Arbor, MI  USA  48109

    National Science Foundation

    1800 G Street, NW
    Washington, DC  USA  20550
  • Authors:
    • OGILVIE, T FRANCIS
  • Publication Date: 1970-10

Media Info

  • Features: References;
  • Pagination: 198 p.
  • Serial:
    • Issue Number: 096

Subject/Index Terms

Filing Info

  • Accession Number: 00011983
  • Record Type: Publication
  • Source Agency: University of Michigan, Ann Arbor
  • Contract Numbers: GK 14375
  • Files: TRIS
  • Created Date: Mar 23 1971 12:00AM