Skip to main content Accessibility help
×
Home

Nonlinear long waves generated by a moving pressure disturbance

  • C. M. Casciola (a1) and M. Landrini (a2)

Abstract

The evolution of long waves generated by a pressure disturbance acting on an initially unperturbed free surface in a channel of finite depth is analysed. Both off-critical and transcritical conditions are considered in the context of the fully nonlinear inviscid problem. The solution is achieved by using an accurate boundary integral approach and a time-stepping procedure for the free-surface dynamics.

The discussion emphasizes the comparison between the present results and those provided by both the Boussinesq and the related Korteweg–de Vries model. For small amplitudes of the forcing, the predictions of the asymptotic theories are essentially confirmed. However, for finite intensities of the disturbance, several new features significantly affect the physical results. In particular, the interaction among different wave components, neglected in the Korteweg–de Vries approximation, is crucial in determining the evolution of the wave system. A substantial difference is indeed observed between the solutions of the Korteweg–de Vries equation and those of both the fully nonlinear and the Boussinesq model. For increasing dispersion and fixed nonlinearity the agreement between the Boussinesq and fully nonlinear description is lost, indicating a regime where dispersion becomes dominant.

Consistently with the long-wave modelling, the transcritical regime is characterized by an unsteady flow and a periodic emission of forward-running waves. However, also in this case, quantitative differences are observed between the three models. For larger amplitudes, wave steepening is almost invariably observed as a precursor of the localized breaking commonly detected in the experiments. The process occurs at the crests of either the trailing or the upstream-emitted wave system for Froude numbers slightly sub- and super-critical respectively.

Copyright

References

Hide All
Akylas, T. R. 1984 On the excitation of long nonlinear water waves by a moving pressure distribution. J. Fluid Mech. 141, 455466.
Baker, G. R., Meiron, D. I. & Orszag S. A. 1989 Generalized vortex methods for free surface flow problems. II: Radiating waves. J. Sci. Comput. 4, 237259.
Bassanini, P., Casciola, C. M., Lancia, M. R. & Piva, R. 1991 A boundary integral formulation for the kinetic field in aerodynamics. Part I Eur. J. Mech. B/Fluids 10, 605627.
Casciola, C. M. & Piva, R. 1990 A boundary integral approach in primitive variables for free surface flows. In Proc. 18th Symp. on Naval Hydrod., pp. 221238. Washington D.C.: National Academy of Sciences.
Cole, S. L. 1985 Transient waves produced by flow past a bump. Wave Motions 7, 579587.
Cooker, M. J., Peregrine, D. H., Vidal, C. & Dold, D. J. 1990 The interaction between a solitary wave and a submerged semicircular cylinder. J. Fluid Mech. 215, 122.
Dold, J. W. 1992 An efficient surface integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90115.
Dold, J. W. & Peregrine, D. H. 1986 An efficient boundary integral method for steep unsteady water waves. In Numerical Methods for Fluid Dynamics II (ed. L. W. Morton and M. J. Baines), pp. 671679. Oxford University Press.
Dommermuth, D. G., Yue, D. K. P., Rapp, R. J., Chann, E. S. & Melville, W. K. 1988 Deep-water plunging breakers: a comparison between potential theory and experiments. J. Fluid Mech. 189, 423442.
Ertekin, R. C., Webster, W. C. & Wehausen, J. V. 1984 Ship generated solitons. In Proc. 15th Symp. on Nav. Hydr., pp. 115. Washington DC: National Academy of Sciences.
Fenton, J. 1972 A ninth-order solution for the solitary wave. J. Fluid Mech. 53, 257271.
Huang, D. D., Sibul, O. J., Webster, W. C., Wehausen, J. V., Wu, D. M. & Wu, T. Y. 1982 In Proc. Conf. on Behaviour of Ships in Restricted Waters, vol. II, pp. 26.126.10. Varna: Bulgarian Ship Hydrodynamics Centre.
Israeli, M. & Orszag, S. 1981 Approximation of radiation boundary conditions. J. Comput. Phys. 41, 115135.
Kevorkian, J. & Yu, J. 1989 Passage through the critical Froude number for shallow water waves over a variable bottom. J. Fluid Mech. 204, 3156.
Lee, S., Yates, G. T. & Wu, T. 1989 Experiments and analyses of upstream—advancing solitary waves generated by moving disturbances. J. Fluid Mech. 199, 569593.
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. I A numerical method of computation. Proc. R. Soc. Lond. A 350 126.
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.
Melville, W. K. & Helfrich, K. R. 1987 Transcritical two—layer flow over topography. J. Fluid Mech. 178, 3152.
Miles, J. W. 1986 Stationary, transcritical channel flow. J. Fluid Mech. 162, 489499.
New, A. L., McIver, P. & Peregrine, D. H. 1985 Computations of overturning waves J. Fluid Mech. 150, 233251.
Roberts, A. J. 1983 A stable and accurate numerical method to calculate the motion of a sharp interface between fluids. IMA J. Appl. Maths 31, 1335.
Segur, H. 1973 The Korteweg—de Vries equation and water waves. J. Fluid. Mech. 59, 721736.
Shen, S. S. 1993 A Course on Nonlinear Waves. Kluwer.
Sidi, A. & Israeli, M. 1988 Quadrature methods for periodic singular and weakly singular fredholm integral equations. J. Sci. Comput. 3, 201231.
Stoker, J. J. 1957 Water Waves. Interscience.
Teles da Silva, A. F. & Peregrine, D. H. 1992 Wave breaking due to moving submerged obstacles. In Proc. IUTAM Symp. on Wave Breaking, Sydney (ed. Banner & Grimshaw), pp. 333340. Springer.
Thews, J. G. & Landweber, L. 1936 US Experimental Model Basin Rep. 408414. Washington DC: Navy Yard.
Tomasson, G. G. & Melville, W. K. 1991 Flow past a constriction in a channel: a modal description J. Fluid Mech. 232, 2145.
Wei, G., Kirby, J. T., Grilli, S. T. & Subramanya, R. 1995 A fully nonlinear Boussinesq model for surface waves. Part 1. highly nonlinear unsteady waves. J. Fluid Mech. 294, 7292.
Vinje, T. & Brevig, P. 1981 Numerical simulations of breaking waves. In Adv. Water Resources 4, 7782.
Wu, D. M. & Wu, T. Y. 1982 Three-dimensional nonlinear long waves due to moving surface pressure. In Proc. 14th Symp. on Nav. Hydr., pp. 103125. Washington DC: National Academy of Sciences.
Wu, T. Y. 1987 Generation of upstream solitons by moving disturbances. J. Fluid Mech. 184, 7599.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

Nonlinear long waves generated by a moving pressure disturbance

  • C. M. Casciola (a1) and M. Landrini (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.