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On Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depth

  • MICHAEL STIASSNIE (a1) and ODIN GRAMSTAD (a2)
Abstract

The non-uniqueness of Zakharov's kernel T(ka, kb, ka, kb) for gravity waves in water of finite depth is resolved. This goal is achieved by the physical insight gained from the study of the induced mean flow generated by two interacting wavetrains.

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Corresponding author
Email address for correspondence: miky@tx.technion.ac.il
References
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Davey, A. & Stewartson, K. 1974 On three-dimensional packets of surface waves. Proc. R. Soc. Lond. A 338 (1613), 101110.
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481500.
Herterich, K. & Hasselmann, K. 1980 Similarity relation for the nonlinear energy-transfer in a finite-depth gravity-wave spectrum. J. Fluid Mech. 97, 215224.
Hogan, S. J., Gruman, I. & Stiassnie, M. 1988 On the changes in phase speed of one train of water-waves in the presence of another. J. Fluid Mech. 192, 97114.
Janssen, P. A. E. M. & Onorato, M. 2007 The intermediate water depth limit of the Zakharov equation and consequences for wave prediction. J. Phys. Oceanogr. 37, 23892400.
Knobloch, E. & Pierce, R. D. 1998 On mean flows associated with travelling water waves. Fluid Dyn. Res. 22 (2), 6171.
Krasitskii, V. P. 1994 On reduced equations in the Hamiltonian theory of weakly nonlinear surface-waves. J. Fluid Mech. 272, 120.
Lavrova, O. T. 1983 On the lateral instability of waves on the surface of a finite-depth fluid. Izv. Atmos. Ocean. Phys. 19, 807810.
Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12, 333336.
Longuet-Higgins, M. S. & Stewart, R. W. 1962 Radiation stress and mass transport in gravity waves, with application to ‘surf beats’. J. Fluid Mech. 13 (4), 481504.
Madsen, P. A. & Fuhrman, D. R. 2006 Third-order theory for bichromatic bi-directional water waves. J. Fluid Mech. 557, 369397.
Mei, C. C., Stiassnie, M. & Yue, D. K. P. 2005 Theory and Applications of Ocean Surface Waves, Part 2: Nonlinear Aspects. World Scientific.
Stiassnie, M. & Shemer, L. 1984 On modifications of the Zakharov equation for surface gravity-waves. J. Fluid Mech. 143, 4767.
Stiassnie, M. & Shemer, L. 1987 Energy computations for evolution of class-I and class-II instabilities of stokes waves. J. Fluid Mech. 174, 299312.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Yuen, H. C. & Lake, B. M. 1982 nonlinear dynamics of deep-water gravity-waves. Adv. Appl. Mech. 22, 67229.
Zakharov, V. 1999 Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid. Eur. J. Mech. B 18 (3), 327344.
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190194.
Zakharov, V. E. & Kharitonov, V. G. 1970 Instability of monochromatic waves on the surface of a liquid of arbitrary depth. J. Appl. Mech. Tech. Phys. 11, 741751.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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