A series of corrugations on the bottom of a layer of water of otherwise uniform depth can have a cooperative effect on incident water waves. The phenomenon is well-known, called Bragg reflection or Bragg resonance. These effects on the normal modes of oscillation in a rectangular tank with corrugated bottom are studied using an asymptotic theory, and by developing an exact theory. The exact theory confirms the essential correctness of the asymptotic results for the slowly varying aspects of the motions. The rapidly varying components are, however, important to the flow near the boundaries. Higher order Bragg resonance, i.e. when the spacing of corrugations is an integer (greater than 1) multiple of half the water wavelength, is examined and the solution regimes (resonance tongues) are constructed using the exact theory.
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ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering
May 31–June 5, 2009
Honolulu, Hawaii, USA
Conference Sponsors:
- Ocean, Offshore and Arctic Engineering Division
ISBN:
978-0-7918-4346-8
PROCEEDINGS PAPER
Bragg Reflection of Water Waves in a Rectangular Channel
Jie Yu,
Jie Yu
North Carolina State University, Raleigh, NC
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Louis N. Howard
Louis N. Howard
Massachusetts Institute of Technology, Cambridge, MA
Search for other works by this author on:
Jie Yu
North Carolina State University, Raleigh, NC
Louis N. Howard
Massachusetts Institute of Technology, Cambridge, MA
Paper No:
OMAE2009-79388, pp. 407-415; 9 pages
Published Online:
February 16, 2010
Citation
Yu, J, & Howard, LN. "Bragg Reflection of Water Waves in a Rectangular Channel." Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. Volume 6: Materials Technology; C.C. Mei Symposium on Wave Mechanics and Hydrodynamics; Offshore Measurement and Data Interpretation. Honolulu, Hawaii, USA. May 31–June 5, 2009. pp. 407-415. ASME. https://doi.org/10.1115/OMAE2009-79388
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