近年來利用數值計算模擬波浪傳遞，以便快速得到流場訊息，然而不同模式在相同條件下，計算所得到的流場訊息也不盡相同。本文利用Lynett & Liu （2004）提出2層型式之布式方程式以及蔡等人(2001)所提出之緩坡模式與試驗在波高、水位波形、振幅波譜等三方面作討論比較。
波高方面在兩模式均不考慮底床摩擦力下，其計算出之波高值在等深段幾乎相同，然而試驗因等深段較長，而且水槽側壁及底床非為光滑，故兩模式計算之波高值均略大於試驗波高值；從波高比較圖發現，二模式在能夠預測出碎波可能發生之區域。水位波形方面，在等深段兩模式計算水位波形幾乎與試驗一樣，但在斜坡上布氏模式能夠表現出水位波形之不對稱性，而緩坡則無法表現出水位波形之不對稱性。振幅波譜方面，兩模式都能預測出主頻發生位置，但布氏能夠計算出二倍頻與三倍頻之能量，而緩坡模式之二倍頻與三倍頻能量則是微量趨近於零。

Numerical simulations have been widely used to study waves propagation over different bathymetry in order to obtain flow fields more efficiently. However, the calculated flow fields by different models would not be the same even under exactly the same input conditions. Therefore, two different models, namely, the multi-layer Bousinessq model developed by Lynett & Liu (2004) and mild-slope equations model presented by Tsai et al. (2001), are used to simulate the evolution of deep water waves on sloping bottoms. In particular, the wave heights, waveforms and amplitude spectra are compared with those of experimental data and discussed.
Based on our results, the wave heights predicted by these two models are almost identical in the uniform water depth region but slightly higher than those of experimental data. It is in part due to the omission of bottom friction in the numerical models. In addition, both models can quite accurately predict the locations of breaking event. Furthermore, the wave forms calculated by these two models match quite well with experimental results in the uniform water depth region. However, on sloping bottoms, the waveforms become asymmetrical due to shoaling process and nonlinear effects and such waveforms can only be reproduced by Boussinesq model. It is not surprising that mild-slope equations model fails to predict such asymmetric waveforms due to its linear assumption in derivation. Similarly, the main frequency can be captured by both models. However, superharmonic modes generated by nonlinearity can only be reproduced by Boussinesq model.

1. Agnon, Y.,Madsen,P . A. and Schaffer,H.,(1999),”A new approach to high order Boussinesq.”, J.Fluid Mech. , vol.399, pp.319-333

2. Berkhoff,J.C.W.,”Computation of combined refraction-diffraction(1972)”,Proceedings of the Thirteenth International Conference on Coastal Engineering,ASCE, pp.471-490

3. Booij,N.,(1981),”Gravity wave on water with non-uniform depth and current.”, Department Civil Enginnering ,Delft University of Technique,Delft,The Netherlands, Report No. 81-1.

4. Ching-Piao Tsai, Hong-Bin Chen, John R.-C. Hsu (2001),”Calculations of wave transformation across the surf zone”,Ocean Engineering ,vol.28, pp.941-955

5. Copeland,G.J.M.,(1985),”A practical alternative to the ‘mild-slope’ wave equation.” Coastal Engineering ,vol.9, pp.125-149

6. Goda,Y.,(1988),”Irregular wave deformation in the surf zone.”,Coastal Engineering in Japan,JSCE 18,pp.13-26

7. Gobbi,M.F. and Kirby J.T.,(2000),”A fully nonlinear Boussinesq model for surface wave. Part 2. Extension to .” ,Coastal Engineering , vol.37 ,pp.57-96

8. Kennedy,A.B.,Chen Q.,Kirdy J.M. and Dalrymple R.A.,(2000),”Boussinesq model of wave transformation,breaking,and runup.I:1D”,Journal of Waterway ,Port,Coastal and Ocean enginnering,ASCE, vol.126,No1,pp.39-47

9. Lynett,P. and Liu,P. L.-F,(2004a),”Amuliti-layer approach to wave modeling.” , Royal Society of London A, in review.

10. Lynett,P. and Liu,P. L.-F,(2004b),”Linear analysis of the N-layer,depth-integrated model.", Coast. Engng. , in review.

11. Madsen,P.A.,Bingham,H.B. and Liu,H.,(2002),”A new Boussinesq method for fully nonlinear waves from shallow to deep water.”, Journal of Fluid Mechanics, vol 462,
pp.1-30

12 Nwogu,O.,(1993),”An alternative form of the Boussinesq equations for modeling the propation of waves form deep to shallow water.” , Journal of Waterway,Port,Coastal and Ocean Engineering ,ASCE, vol 119(6), pp.618-638

13. Peregrine,D.H.,(1967),”Long waves on a beach.”, Journal of Fluid Mechanics,vol.27(4), pp.815-827

14. Raddar,A.C.,(1979),”On the parabolic equation method for water wave propagation.”, Journal of Fluid Mechanics ,vol.95,pp.159-176

15. Watanabe,A.,Dibajnia,M.,(1988),”A numerical model of wave deformation in surf zone.” Proceedings of the twenty-first International Conference on Coastal Engineering,ASCE, pp.578-587

16. Watanabe,A.,Maruyama,K.,(1986),”Numerical modeling of nearshore wave field under combined refraction,diffraction and breaking.”,Coastal Engineering in Japan,JSCE 29, pp.19-39

17. Wei,G.,Kirby J.T.(1995),”Time-dependent numerical code for extend Boussinesq equations.”, Journal of Waterway,Port,Coastal and Ocean Engineering ,ASCE, vol 121(6), pp.251-263