COMPUTER EXTENSION AND ANALYTIC CONTINUATION OF STOKES EXPANSION FOR GRAVITY WAVES

Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of approximants. The method is valid in principle for any finite value of the wavelength, and solutions of high accuracy can be obtained for most values of the wave height and water depth. (Modified author abstract)

  • Supplemental Notes:
    • Also published in the Journal of Fluid Mechanics, V62, p 553-578, 1974.
  • Corporate Authors:

    Stanford University

    Department of Aeronautics and Astronautics
    Stanford, CA  USA  94305

    Air Force Office of Scientific Research

    Bolling AFB
    Washington, DC  USA  20332
  • Authors:
    • Schwartz, L W
  • Publication Date: 1973-4-25

Media Info

  • Pagination: 38 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00095110
  • Record Type: Publication
  • Source Agency: National Technical Information Service
  • Report/Paper Numbers: Intrm Rpt
  • Contract Numbers: F44620-69-C-0036
  • Files: TRIS
  • Created Date: May 29 1975 12:00AM