Hostname: page-component-5c6d5d7d68-ckgrl Total loading time: 0 Render date: 2024-08-09T14:25:56.234Z Has data issue: false hasContentIssue false
  • English
  • Français

On the quadratic effect of random gravity waves on a vertical boundary

Published online by Cambridge University Press:  26 April 2006

P. D. Sclavounos
P. D. Sclavounos
Affiliation:
Department of Ocean Engineering, MIT, Cambridge MA 02139. USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The quadratic effect of random gravity waves in the vicinity of a reflecting boundary is studied. It is shown that in a stochastic wave environment, surface wave effects proportional to the square of the wave amplitude depend upon the third-order free-surface perturbation. Expressions are derived for the quadratic frequency spectrum of the hydrodynamic pressure in the fluid domain in unidirectional and standing waves reflected off a vertical wall. Computations of the spectrum reveal the importance of the effect contributed by the third-order solution, which is found to be at least of comparable magnitude to the corresponding effect obtained from the solution of the second-order problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 475 - 489
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Faltinsen, O. M. 1990 Sea Loads on Ships and Offshore Structures. Cambridge University Press.
Hasselmann, K. 1962 On the non-linear energy transfer in a gravity wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–500.Google Scholar
Kinsman, B. 1965 Wind Waves. Dover.
Lighthill, J. 1959 Fourier Series and Generalised Functions. Cambridge University Press.
Longuet-Higgins, M. S. 1963 The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, 459–480.Google Scholar
Ogilvie, T. F. 1983 Second order hydrodynamic effects on ocean platforms In Proc. Intl Workshop on Ship Platform Motions, University of California, Berkeley.
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.Google Scholar
Tick, L. J. 1959 A non-linear random model of gravity waves. J. Maths Mech. 8, 643–652.Google Scholar