Enhanced Computational Methods for Nonlinear Hamiltonian Wave Dynamics. Part II: New Results

Jorge F. Willemsen Rosenstiel School of Marine and Atmospheric Science, Division of Applied Marine Physics, University of Miami, Miami, Florida

Search for other papers by Jorge F. Willemsen in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

It has been noted that the nonlinear Hamiltonian dynamical equations describing surface waves are of convolution form in a version derived by Krasitskii, and thus they are amenable to numerical calculations using fast Fourier transform techniques. In this paper new results regarding the nature of the solutions are presented and numerical instabilities that may develop are discussed. Additionally various ways of displaying features of the nonlinear wave evolution are explored within the context of specific examples.

Corresponding author address: Dr. Jorge F. Willemsen, Rosenstiel School of Marine and Atmospheric Science, Division of Applied Marine Physics, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. Email: jorge@maya.rsmas.miami.edu

Abstract

It has been noted that the nonlinear Hamiltonian dynamical equations describing surface waves are of convolution form in a version derived by Krasitskii, and thus they are amenable to numerical calculations using fast Fourier transform techniques. In this paper new results regarding the nature of the solutions are presented and numerical instabilities that may develop are discussed. Additionally various ways of displaying features of the nonlinear wave evolution are explored within the context of specific examples.

Corresponding author address: Dr. Jorge F. Willemsen, Rosenstiel School of Marine and Atmospheric Science, Division of Applied Marine Physics, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. Email: jorge@maya.rsmas.miami.edu

Save
  • Banner, M. L., and Tian X. , 1998:: On the determination of the onset of breaking for modulating surface gravity water waves. J. Fluid Mech., 267 , 107137.

    • Search Google Scholar
    • Export Citation
  • Craig, W., and Worfolk P. A. , 1995:: An integrable normal-form for water waves in infinite depth. Physica D, 84 , 513531.

  • Dold, J. W., and Peregrine D. H. , 1986:: Water-wave modulation. Proc. 20th Intl. Conf. Coastal Eng., Taipei, Taiwan, ASCE, 163–175.

  • Dyachenko, A. I., and Zakharov V. E. , 1994:: Is free-surface hydrodynamics an integrable system? Phys. Lett., A190 , 144148.

  • Komen, G. J., Cavaleri L. , Donelan M. , Hasselmann K. , Hasselmann S. , and Janssen P. A. E. M. , 1994:: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 528 pp.

    • Search Google Scholar
    • Export Citation
  • Krasitskii, V. P., 1994:: On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech., 272 , 121.

  • Longuet-Higgins, M. S., 1978:: On the dynamics of steep gravity waves in deep water. Proc. NATO Conf. on Turbulent Fluxes through the Sea Surface, Wave Dynamics, and Prediction, Marseilles, France, NATO Special Program Panel on Air–Sea Interactions, 199–220.

    • Search Google Scholar
    • Export Citation
  • Magnusson, A. K., Donelan M. A. , and Drennan W. M. , 1999:: On estimating extremes in an evolving wave field. Coastal Eng., 36 , 147163.

  • Phillips, O. M., 1985:: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid. Mech., 156 , 505531.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pond, S., and Pickard G. L. , 1983:: Introductory Dynamical Oceanography. 2d ed. Pergamon Press, 349 pp.

  • Willemsen, J. F., 1998:: Enhanced Computational Methods for Nonlinear Hamiltonian Wave Dynamics. J. Atmos. Oceanic Technol., 15 , 15171523.

    • Search Google Scholar
    • Export Citation
  • Zakharov, V. E., 1968:: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Technol. Phys., 9 , 190194.

    • Search Google Scholar
    • Export Citation
  • Kuznetsov, E. A., 1997:: Hamiltonian formalsim for nonlinear waves, USP FIZ NAUK. 167. 11371167.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 182 25 2
PDF Downloads 39 13 0