A Variational Method in Potential Flows with a Free Surface

Abstract

The steady oscillatory irrotational motion of an inviscid incompressible fluid is described by a boundary-value problem of elliptic type. A variational form of this problem has been made here the basis of a numerical method. The problem is simplified assuming that the amplitudes of the generated waves are small compared with their wave lengths. The numerical satisfaction of the radiation boundary condition has been investigated. Some sample problems with known solutions have been treated first in order to test the method. All the results for two-dimensional motion and for heaving motion of an axisymmetric body in infinite or finite depths show very good agreement with existing results. In addition, some diffraction problems in two dimensions with homogeneous fluid or stratified fluids are solved, and also a problem with nonuniform depth.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1972
Accession Number
AD0755465

Entities

People

  • Kwang J. Bai

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Bessel Functions
  • Boundary Value Problems
  • Cartesian Coordinates
  • Complex Variables
  • Computer Programs
  • Coordinate Systems
  • Differential Equations
  • Engineering
  • Equations
  • Geometry
  • Pressure Distribution
  • Standing Waves
  • Stratified Fluids
  • Surface Waves
  • Three Dimensional
  • Two Dimensional
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.