Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T06:46:34.276Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on standing waves in a rectangular tank with a corrugated bed

Published online by Cambridge University Press:  16 July 2015

Patrick D. Weidman ,
Andrzej Herczynski ,
Jie Yu  and
Louis N. Howard
Patrick D. Weidman*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA
Andrzej Herczynski
Affiliation:
Department of Physics, Boston College, Chestnut Hill, MA 92467-3811, USA
Jie Yu
Affiliation:
Civil Engineering Program, Department of Mechanical Engineering, School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, NY 11790, USA
Louis N. Howard
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental investigation of resonant standing water waves in a rectangular tank with a corrugated bottom is reported. The study was stimulated by the theory of Howard & Yu (J. Fluid Mech., vol. 593, 2007, pp. 209–234) predicting the existence of normal modes that can be significantly affected by Bragg reflection/scattering. As a result, the amplitude of the standing waves (normal modes) varies exponentially along the entire length of the tank, or from the centre out in each direction, depending on the phase of the corrugations at the tank endwalls. Experiments were conducted in a 5 m tank fitted with a sinusoidal bottom with one adjustable endwall. Waves were excited by small-amplitude sinusoidal horizontal movement of the tank using an electrical motor drive system. Simultaneous time-series data of standing oscillations were recorded at well-separated positions along the tank to measure the growth in amplitude. Waveforms over a section of the tank were filmed through the transparent acrylic walls. Except for very shallow depths and near the tank endwalls, the experimental measurements of resonant frequencies, mean wavelengths, free-surface waveforms and amplitude growth are found in essential agreement with the Bragg resonant normal mode theory.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 122 - 150
Check for updates
Copyright
© 2015 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

Bagnold, R. A. 1946 Motion of waves in shallow water – interaction between waves and sand bottoms. Proc. R. Soc. Lond. A 187, 1–18.Google Scholar
Bailard, J. A., DeVries, J. W. & Kirby, J. T. 1992 Considerations in using Bragg reflection for storm erosion protection. J. Waterway Port Coastal Ocean Engng 118, 62–74.CrossRefGoogle Scholar
Benjamin, T. B., Boczar-Karakiewicz, B. & Pritchard, W. G. 1987 Reflections of water waves in a channel with corrugated bed. J. Fluid Mech. 185, 249–274.CrossRefGoogle Scholar
Davies, A. G.1980 Some interactions between surface water waves and ripples and dunes on the seabed. Part 1: the wave-induced flow over seabed topography; Part 2: the reflection of incident wave energy by seabed topography. Institute of Oceanographic Sciences Report No. 108, p. 134.Google Scholar
Davies, A. G. 1982 The reflection of wave energy by undulations of the seabed. Dyn. Atmos. Oceans 6, 207–232.CrossRefGoogle Scholar
Davies, A. G. & Heathershaw, A. D.1983 Surface wave propagation over sinusoidally varying topography: theory and observation. Parts 1 and 2. Institute of Oceanographic Sciences Report No. 159, p. 181.Google Scholar
Davies, A. G. & Heathershaw, A. D. 1984 Surface wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.CrossRefGoogle Scholar
Davis, A. M. J. & Weidman, P. D. 2000 Asymptotic estimates for two-dimensional sloshing modes. Phys. Fluids 12, 971–978.CrossRefGoogle Scholar
Heathershaw, A. D. 1982 Seabed–wave resonance and sand bar growth. Nature 296, 343–345.CrossRefGoogle Scholar
Henderson, D. M. & Hammack, J. L. 1987 Experiments on ripple instabilities. Part 1. Resonant triads. J. Fluid Mech. 184, 15–47.CrossRefGoogle Scholar
Howard, L. N. & Yu, J. 2007 Normal modes of a rectangular tank with corrugated bottom. J. Fluid Mech. 593, 209–234.CrossRefGoogle Scholar
Kirby, J. T. 1986a A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171–186.CrossRefGoogle Scholar
Kirby, J. T. 1986b On the gradual reflection of weakly nonlinear Stokes waves in regions of varying topography. J. Fluid Mech. 162, 187–209.CrossRefGoogle Scholar
Kirby, J. T. 1993 A note on Bragg scattering of surface waves by sinusoidal bars. Phys. Fluids 5, 380–386.CrossRefGoogle Scholar
Kirby, J. T. & Anton, J. P. 1990 Bragg reflection of waves by artificial bars. In Proceedings of the 22nd International Conference on Coastal Engineering, Delft, pp. 757–768. ASCE.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
Massel, S. R. 1996 Ocean Surface Waves: Their Physics and Prediction, Advanced Series on Ocean Engineering, vol. 11. World Scientific.Google Scholar
Mei, C. C. 1985 Resonant reflection of surface waves by periodic sandbars. J. Fluid Mech. 152, 315–337.CrossRefGoogle Scholar
Milne-Thomson, L. M. 1962 Theoretical Hydrodynamics. Macmillan.Google Scholar
O’Hare, T. J. & Davies, A. G. 1993 Sand bar evolution beneath partially-standing waves: laboratory experiments and model simulations. Cont. Shelf Res. 13, 1149–1181.CrossRefGoogle Scholar
Riley, N. 1984 Progressive surface waves on a liquid of non-uniform depth. Wave Motion 6, 15–22.CrossRefGoogle Scholar
Sammarco, P., Mei, C. C. & Trulsen, K. 1994 Nonlinear resonance of free surface waves in a current over a sinusoidla bottom: a numerical study. J. Fluid Mech. 179, 377–405.CrossRefGoogle Scholar
Weidman, P. D. & Kliakhandler, I. 2014 Gravitational oscillations of a capped liquid–air column. Phys. Fluids 26, 04710,1–21.CrossRefGoogle Scholar
Xu, D., Zhiliang, L. & Liao, S. 2015 Equilibrium states of class-I resonant wave system. Eur. J. Mech. (B/Fluids) 50, 38–51.CrossRefGoogle Scholar
Yu, J. & Howard, L. N. 2010 On higher order resonance of water waves by bottom corrugations. J. Fluid Mech. 659, 484–504.CrossRefGoogle Scholar
Yu, J. & Howard, L. N. 2012 Exact Floquet theory for waves over arbitrary periodic topographies. J. Fluid Mech. 712, 451–470.CrossRefGoogle Scholar
Yu, J. & Mei, C. C. 2000a Do longshore bars shelter the shore? J. Fluid Mech. 404, 251–270.CrossRefGoogle Scholar
Yu, J. & Mei, C. C. 2000b Formation of sand bars under surface waves. J. Fluid Mech. 416, 315–348.CrossRefGoogle Scholar
Yu, J. & Zheng, G. 2012 Exact solutions for wave propagation over a patch of large bottom corrugations. J. Fluid Mech. 713, 362–375.CrossRefGoogle Scholar