On three-dimensional packets of surface waves

@article{Davey1974OnTP,
  title={On three-dimensional packets of surface waves},
  author={A. Davey and K. Stewartson},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1974},
  volume={338},
  pages={101 - 110}
}
  • A. Davey, K. Stewartson
  • Published 1974
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
In this note we use the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wave-packet of wavenumber k on water of finite depth. The equations are used to study the stability of the uniform Stokes wavetrain to small disturbances whose length scale is large compared with 2π/k. The stability criterion obtained is identical with that derived by Hayes under the more restrictive requirement that the… Expand
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References

SHOWING 1-7 OF 7 REFERENCES
Nonlinear Modulation of Gravity Waves
  • 438
  • Highly Influential
Group velocity and nonlinear dispersive wave propagation
  • W. Hayes
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1973
  • 98
  • Highly Influential
A non-linear instability theory for a wave system in plane Poiseuille flow
  • 398
Two-timing, variational principles and waves
  • 135
  • PDF
Discussion: some results from wave pulse experiments
  • J. E. Feir
  • Physics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1967
  • 53
  • Highly Influential
The disintegration of wave trains on deep water Part 1. Theory
  • 1,730
  • Highly Influential