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Effects of channel cross-sectional geometry on long wave generation and propagation

Teng, Michelle H. and Wu, Theodore Y. (1997) Effects of channel cross-sectional geometry on long wave generation and propagation. Physics of Fluids, 9 (11). pp. 3368-3377. ISSN 1070-6631. doi:10.1063/1.869449.

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Joint theoretical and experimental studies are carried out to investigate the effects of channel cross-sectional geometry on long wave generation and propagation in uniform shallow water channels. The existing channel Boussinesq and channel KdV equations are extended in the present study to include the effects of channel sidewall slope at the waterline in the first-order section-mean equations. Our theoretical results show that both the channel cross-sectional geometry below the unperturbed water surface (characterized by a shape factor kappa) and the channel sidewall slope at the waterline (represented by a slope factor gamma) affect the wavelength (lambda) and time period (Ts) of waves generated under resonant external forcing. A quantitative relationship between lambda, Ts, kappa, and gamma is given by our theory which predicts that, under the condition of equal mean water depth and equal mean wave amplitude, lambda and Ts increase with increasing kappa and gamma. To verify the theoretical results, experiments are conducted in two channels of different geometries, namely a rectangular channel with kappa[equivalent]1, gamma=0 and a trapezoidal channel with kappa=1.27, gamma=0.16, to measure the wavelength of free traveling solitary waves and the time period of wave generation by a towed vertical hydrofoil moving with critical speed. The experimental results are found to be in broad agreement with the theoretical predictions.

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Additional Information:© 1997 American Institute of Physics. (Received 3 February 1997; accepted 15 July 1997) This work was partly supported by the Hawaiian Sea Grant through NOAA Grant No. NA89AA-D-SG063 and by the National Science Foundation Grant No. CMS-9503620. The authors are grateful to the reviewers for their helpful comments and suggestions.
Subject Keywords:channel flow; Korteweg-de Vries equation; surface waves (fluid)
Issue or Number:11
Record Number:CaltechAUTHORS:TENpof97
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9143
Deposited By: Archive Administrator
Deposited On:01 Nov 2007
Last Modified:08 Nov 2021 20:56

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