On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface

Abstract

Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wave instability. To fix that problem we introduce the canonical Hamiltonian transform from original physical variables to new variables for which instability is absent. We found the choice of such transform is unique.

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Document Details

Document Type
Technical Report
Publication Date
May 31, 2004
Accession Number
ADA427105

Entities

People

  • Pavel M. Lushnikov
  • Vladimir E. Zakharov

Organizations

  • University of Arizona

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Complex Variables
  • Computational Fluid Dynamics
  • Computational Science
  • Deep Water
  • Dynamics
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluids
  • Numerical Analysis
  • Shallow Water
  • Short Wavelengths
  • Two Dimensional
  • Two Dimensional Flow
  • Water
  • Wave Equations

Readers

  • Calculus or Mathematical Analysis