SEPARATION OF LOW-FREQUENCY WAVES BY AN ANALYTICAL METHOD

Abstract

A new method for separating low-frequency waves in time domain is proposed by constructing the analytical signals of the measured waves. Using three simultaneous wave records, the time series of incident bound, free and reflected low-frequency waves can be obtained by the present method. This method is only suitable for separating monochromatic low-frequency waves. The applicability of the method is examined by numerical tests. The results show that the present method can give accurate results over sloping beaches when water depth (kh) is larger than 0.2. Then, the present method is used to study an experiment of low-frequency waves over a mild slope beach.
 
 
 References
 
 Bakkenes, H.J. 2002. Observation and separation of bound and free low-frequency waves in the nearshore zone, in Faculty of Civil Engineering and Geosciences. Delft University of Technology: Delft.
 
 Baldock, T.E., D.A., Huntley, P.A.D., Bird, T.O., Hare, and G.N., Bullock. 2000. Breakpoint generated surf beat induced by bichromatic wave groups. Coastal Engineering. 30 (2-4): 213-242.
 http://dx.doi.org/10.1016/S0378-3839(99)00061-7
 
 Battjes, J.A., Bakkenes, H.J., Janssen, T.T., van Dongeren, A.R. 2004. Shoaling of subharmonic gravity waves. J. Geophys. Res., 109(C2): C02009.
 http://dx.doi.org/10.1029/2003JC001863
 
 Bowers, E.C. 1977. Harbour resonance due to set-down beneath wave groups. Journal of Fluid Mechanics. 79: 71-92.
 http://dx.doi.org/10.1017/S0022112077000044
 
 Cohen, L. 1995. Time Frequency Analysis: Theory and Applications. Prentice Hall Englewood Cliffs, New Jersey.
 
 Dong, G.H., X.Z., Ma, M., Perlin, Y.X., Ma, B., Yu, and G., Wang. 2009. Experimental Study of long wave generation on sloping bottoms. Coastal Engineering, 56(1), 82-89.
 http://dx.doi.org/10.1016/j.coastaleng.2008.10.002
 
 Kamphuis, J.W. 2000. Designing for low frequency waves. Proceedings of 27th International Conference on Coastal Engineering. Sydney, Australian. 1434-1447.
 
 Kostense, J.K. 1984. Measurements of surf beat and set-down beneath wave groups. Proceedings of 19th International Conference on Coastal Engineering. Houston, USA. 724-740.
 
 Longuet-Higgins, M.S. and R.W., Stewart. 1962. Radiation stress and mass transport in gravity waves with application to 'surfbeat'. Journal of Fluid Mechanics. 13: 481-504
 http://dx.doi.org/10.1017/S0022112062000877
 
 Mallat, S. 1999. A Wavelet Tour of Signal Processing. Academic Press. PMCid:407895
 
 Nagai, T., N., Hashimoto, T., Asai, et al. 1994. Relationship of a moored vessel in a harbor and a long wave caused by wave groups. Proceedings of 17th International Conference on Coastal Engineering. Kobe, Japan. 847-861.
 
 Schäffer, H.A. 1993. Second-orderwavemaker theory for irregularwaves.Ocean Engineering. 23 (1), 47-88.
 http://dx.doi.org/10.1016/0029-8018(95)00013-B
 
 Symonds, G.D.A., D.A., Huntley, and A.J., Bowen. 1982. Two-dimensional surf beat-long-wave generation by a time-varying breakpoint. Journal of Geophysical Research. 87(C1): 492-498.
 http://dx.doi.org/10.1029/JC087iC01p00492
 
 Yu, J. and C.C., Mei. 2000. Formation of sand bars under surface waves. Journal of Fluid Mechanics. 416: 315-348.
 http://dx.doi.org/10.1017/S0022112000001063