Propagation of solitary waves through signicantly curved shallow water channels
Propagation of solitary waves in curved shallow water channels of constant depth and width is investigated by carrying out numerical simulations based on the generalized weakly nonlinear and weakly dispersive Boussinesq model. The objective is to investigate the effects of channel width and bending sharpness on the transmission and reflection of long waves propagating through significantly curved channels. Our numerical results show that, when travelling through narrow channel bends including both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted almost completely with little reflection and scattering. For wide channel bends, we find that, if the bend is rounded and smooth, a solitary wave is still fully transmitted with little backward reflection, but the transmitted wave will no longer preserve the shape of the original solitary wave but will disintegrate into several smaller waves. For solitary waves travelling through wide sharp-cornered 90°-bends, wave reflection is seen to be very significant, and the wider the channel bend, the stronger the reflected wave amplitude. Our numerical results for waves in sharp-cornered 90°-bends revealed a similarity relationship which indicates that the ratios of the transmitted and reflected wave amplitude, excess mass and energy to the original wave amplitude, mass and energy all depend on one single dimensionless parameter, namely the ratio of the channel width b to the effective wavelength [lambda][sub]e. Quantitative results for predicting wave transmission and reflection based on b/[lambda][sub]e are presented.
Additional Information"Reprinted with the permission of Cambridge University Press." (Received 20 September 1996 and in revised form 18 November 1997). The authors wish to thank Professor Allen Chwang at the Hong Kong University, Professor Philip Liu at Cornell University and Professor Harry Yeh at the University of Washington for providing us with their valuable comments. The authors appreciate greatly the helpful discussions with Professors C. C. Mei, R. Grimshaw, C.-S. Yih, S. J. Lee, and S. H. Kwon at the 2nd International Conference on Hydrodynamics in Hong Kong. We are also grateful to the reviewers for their helpful comments, especially for those on the effect of wavelength and on the important results by Rostafinski (1972, 1976) and by Kirby et al. (1994). Computations in the present study were performed on Cray c90 at the San Diego Supercomputer Center (SDSC) which is supported by the US National Science Foundation.
Published - SHIjfm98.pdf