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Evolution of long water waves in variable channels

Published online by Cambridge University Press:  26 April 2006

Michelle H. Teng  and
Theodore Y. Wu
Michelle H. Teng
Affiliation:
Engineering Science, 104-44, California Institute of Technology, Pasadena, CA 91125, USA Present address: Department of Civil Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA.
Theodore Y. Wu
Affiliation:
Engineering Science, 104-44, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 266 , 10 May 1994 , pp. 303 - 317
Copyright
© 1994 Cambridge University Press

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