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Evolution of long water waves in variable channels

Teng, Michelle H. and Wu, Theodore Y. (1994) Evolution of long water waves in variable channels. Journal of Fluid Mechanics, 266 . pp. 303-317. ISSN 0022-1120. doi:10.1017/S0022112094001011.

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This paper applies two theoretical wave models, namely the generalized channel Boussinesq (gcB) and the channel Korteweg–de Vries (cKdV) models (Teng & Wu 1992) to investigate the evolution, transmission and reflection of long water waves propagating in a convergent–divergent channel of arbitrary cross-section. A new simplified version of the gcB model is introduced based on neglecting the higher-order derivatives of channel variations. This simplification preserves the mass conservation property of the original gcB model, yet greatly facilitates applications and clarifies the effect of channel cross-section. A critical comparative study between the gcB and cKdV models is then pursued for predicting the evolution of long waves in variable channels. Regarding the integral properties, the gcB model is shown to conserve mass exactly whereas the cKdV model, being limited to unidirectional waves only, violates the mass conservation law by a significant margin and bears no waves which are reflected due to changes in channel cross-sectional area. Although theoretically both models imply adiabatic invariance for the wave energy, the gcB model exhibits numerically a greater accuracy than the cKdV model in conserving wave energy. In general, the gcB model is found to have excellent conservation properties and can be applied to predict both transmitted and reflected waves simultaneously. It also broadly agrees well with the experiments. A result of basic interest is that in spite of the weakness in conserving total mass and energy, the cKdV model is found to predict the transmitted waves in good agreement with the gcB model and with the experimental data available

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Additional Information:© 1994 Cambridge University Press. Received September 1 1992; revised November 16 1993. This work was partly supported by NSF Grant 4DMS-8901440 and its preceding NSF Grant MSM-8706045. We are indebted to the referees for some interesting discussions on numerical results in comparison with the paper by Kirby & Vengayil.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5076
Deposited By: Lindsay Cleary
Deposited On:28 Sep 2006
Last Modified:08 Nov 2021 20:22

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