COMPARISON OF NUMERICAL AND PERTURBATION SOLUTIONS OF TWO- DIMENSIONAL NONLINEAR WATER-WAVE PROBLEMS

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite- difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstearm waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

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  • Corporate Authors:

    Society of Naval Architects and Marine Engineers

    601 Pavonia Avenue
    Jersey City, NJ  USA  07306-2907
  • Authors:
    • Salvesen, N
    • von Kerczek, C
  • Publication Date: 1976-9

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  • Accession Number: 00148189
  • Record Type: Publication
  • Source Agency: Society of Naval Architects and Marine Engineers
  • Files: TRIS
  • Created Date: Feb 16 1977 12:00AM