Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-23T15:26:13.370Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact solutions for wave propagation over a patch of large bottom corrugations

Published online by Cambridge University Press:  17 October 2012

Jie Yu  and
Guangfu Zheng
Jie Yu*
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
Guangfu Zheng
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
*
†Email address for correspondence: jie_yu@ncsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Applying the Floquet theory for linear motions (Howard & Yu, J. Fluid Mech., vol. 593, 2007, pp. 209–234) to the problem of wave propagation over a patch of periodic bottom corrugations in an otherwise flat seabed, we show that exact solutions to this scattering problem can be constructed without any constraint on the bottom amplitude and/or slope. These solutions are able to describe both the slowly and fast varying aspects of the flow, in contrast to the analyses based on the general ideas of slowly varying waves. We use as an example the well-studied Bragg scattering by a patch of bottom corrugations to present some quantitative results and comparisons with experimental data.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 362 - 375
Copyright
©2012 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

Athanassoulis, G. A. & Belibassakis, K. A. 1999 A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions. J. Fluid Mech. 389, 275–301.Google Scholar
Dalrymple, R. A. & Kirby, J. T. 1986 Water waves over ripples. J. Waterways Port Coast. Ocean Engng 112, 309–319.Google Scholar
Davies, A. G. 1982 The reflection of wave energy by undulations on the seabed. Dyn. Atmos. Oceans 6, 207–232.Google Scholar
Davies, A. G. & Heathershaw, A. D. 1983 Surface wave propagation over sinusoidally varying topography: theory and observation. Institute of Oceanographic Sciences report 159.Google Scholar
Davies, A. G. & Heathershaw, A. D. 1984 Surface wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.Google Scholar
Goda, Y & Suzuki, Y. 1977 Estimation of incident and reflected waves in random wave experiments. In Proc. 15th Intl Conf. on Coastal Engng, 1976, pp. 828–845. ASCE.Google Scholar
Hara, T. & Mei, C. C. 1987 Bragg scattering of surface waves by periodic bars: theory and experiment. J. Fluid Mech. 178, 221–241.Google Scholar
Heathershaw, A. D. 1982 Seabed-wave resonance and sand bar growth. Nature 296, 343–345.Google Scholar
Howard, L. N. & Yu, J. 2007 Normal modes of a rectangular tank with corrugated bottom. J. Fluid Mech. 593, 209–234.Google Scholar
Kirby, J. T. 1986 A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171–186.Google Scholar
Liu, P. L.-F. 1987 Resonant reflection of water waves in a long channel with corrugated boundaries. J. Fluid Mech. 179, 371–381.Google Scholar
Liu, Y. & Yue, D. K. P. 1998 On generalized Bragg scattering of surface waves by bottom ripples. J. Fluid Mech. 356, 297–326.CrossRefGoogle Scholar
Mattioli, F. 1990 Resonance reflection of a series of submerged breakwaters. Il Nuovo Cimento C 13, 823–833.Google Scholar
Mattioli, F. 1991 Resonance reflection of surface waves by non-sinusoidal bottom undulations. Appl. Ocean Res. 13, 49–53.Google Scholar
Mei, C. C. 1985 Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech. 152, 315–337.Google Scholar
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.Google Scholar
Mei, C. C., Hara, T. & Yu, J. 2001 Longshore bars and Bragg resonance. In Geomorphological Fluid Mechanics (ed. Balmforth, N. & Provenzale, A.), Lecture Notes in Physics , vol. 582, chap. 20, pp. 500–527. Springer.Google Scholar
Nayfeh, A. H. & Hawwa, M. A. 1994 Interaction of surface gravity waves on a non-uniformly periodic seabed. Phys. Fluids 6, 209–213.Google Scholar
O’Hare, T. J. & Davies, A. G. 1992 A new model for surface wave propagation over undulating topography. Coast. Engng 18, 251–266.Google Scholar
Rey, V. 1992 Propagation and local behavior of normal incident gravity waves over varying topographies. Eur. J. Mech. B 11, 213–232.Google Scholar
Yu, J. & Howard, L. N. 2010 On higher order Bragg resonance of water waves by bottom corrugations. J. Fluid Mech. 659, 484–504.Google Scholar
Yu, J. & Howard, L. N. 2012 Exact Floquet theory for waves over arbitrary periodic topographies. J. Fluid Mech. 712, 451–470.Google Scholar
Yu, J. & Mei, C. C. 2000 Do longshore bars shelter the shore? J. Fluid Mech. 404, 251–268.Google Scholar