Experiments on standing waves in a rectangular tank with a corrugated bed
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 affect...
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Published in | Journal of fluid mechanics Vol. 777; pp. 122 - 150 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
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Cambridge, UK
Cambridge University Press
25.08.2015
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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. |
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AbstractList | 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. 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. 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. |
Author | Weidman, Patrick D. Yu, Jie Howard, Louis N. Herczynski, Andrzej |
Author_xml | – sequence: 1 givenname: Patrick D. surname: Weidman fullname: Weidman, Patrick D. email: weidman@colorado.edu organization: Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA – sequence: 2 givenname: Andrzej surname: Herczynski fullname: Herczynski, Andrzej organization: Department of Physics, Boston College, Chestnut Hill, MA 92467-3811, USA – sequence: 3 givenname: Jie surname: Yu fullname: Yu, Jie organization: Civil Engineering Program, Department of Mechanical Engineering, School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, NY 11790, USA – sequence: 4 givenname: Louis N. surname: Howard fullname: Howard, Louis N. organization: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA |
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Cites_doi | 10.1017/jfm.2012.460 10.1017/S0022112097007969 10.1017/S0022112094003940 10.1017/S0022112099007168 10.1017/S0022112000001063 10.1017/S0022112086001994 10.1017/S0022112087003161 10.1063/1.4870761 10.1017/S0022112085000714 10.1063/1.870352 10.1061/(ASCE)0733-950X(1992)118:1(62) 10.1016/0165-2125(84)90019-2 10.1017/S0022112087002799 10.1016/0377-0265(82)90029-X 10.1063/1.858861 10.1017/S0022112007008695 10.1017/S0022112086002008 10.1038/296343a0 10.1017/S0022112010002582 10.1017/S0022112084001671 10.1017/jfm.2012.432 10.1016/j.euromechflu.2014.10.006 10.1098/rspa.1946.0062 10.1016/0278-4343(93)90047-2 |
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Title | Experiments on standing waves in a rectangular tank with a corrugated bed |
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