EVOLUTION OF LONG WATER-WAVES IN VARIABLE CHANNELS

This paper applies two theoretical wave models, namely the generalized channel Boussinesq (gcB) and the channel Korteweg-de Vries (cKdV) mod els (Teng & Wu 1992) to investigate the evolution, transmission and re flection of long water waves propagating in a convergent-divergent cha nnel of arbitrary cross-section. A new simplified version of the gcB m odel is introduced based on neglecting the higher-order derivatives of channel variations. This simplification preserves the mass conservati on property of the original gcB model, yet greatly facilitates applica tions and clarifies the effect of channel cross-section. A critical co mparative study between the gcB and cKdV models is then pursued for pr edicting the evolution of long waves in variable channels. Regarding t he integral properties, the gcB model is shown to conserve mass exactl y whereas the cKdV model, being limited to unidirectional waves only, violates the mass conservation law by a significant margin and bears n o waves which are reflected due to changes in channel cross-sectional area. Although theoretically both models imply adiabatic invariance fo r the wave energy, the gcB model exhibits numerically a greater accura cy than the cKdV model in conserving wave energy. In general, the gcB model is found to have excellent conservation properties and can be ap plied to predict both transmitted and reflected waves simultaneously. It also broadly agrees well with the experiments. A result of basic in terest is that in spite of the weakness in conserving total mass and e nergy, the cKdV model is found to predict the transmitted waves in goo d agreement with the gcB model and with the experimental data availabl e.