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Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves

DOI: 10.4236/am.2018.92010, PP. 138-152

Keywords: Turbulence, Plunging Breaker, Time Series, Cross-Correlation, Relative Phase, Phase Velocity

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Free surface elevation time series of breaking water waves were measured in a laboratory flume. This was done in order to analyze changes in wave characteristics as the waves propagated from deep water to the shore. A pair of parallel- wire capacitive wave gages was used to simultaneously measure free surface elevations at different positions along the flume. One gage was kept fixed near the wave generator to provide a reference while the other was moved in steps of 0.1 m in the vicinity of the break point. Data from these two wave gages measured at the same time constitute station-to-station free surface elevation time series. Fast Fourier Transform (FFT) based cross-correlation techniques were employed to determine the time lag between each pair of the time series. The time lag was used to compute the phase shift between the reference wave gage and that at various points along the flume. Phase differences between two points spaced 0.1 m apart were used to calculate local mean wave phase velocity for a point that lies in the middle. Results show that moving from deep water to shallow water, the measured mean phase velocity decreases almost linearly from about 1.75 m/s to about 1.50 m/s at the break point. Just after the break point, wave phase velocity abruptly increases to a maximum value of 1.87 m/s observed at a position 30 cm downstream of the break point. Thereafter, the phase velocity decreases, reaching a minimum of about 1.30 m/s.


[1]  Huntley, D.A. (1980) Edge Waves in a Crescentic Bar System. In: S.B. McCain, Ed., The Coastline of Canada, Proceedings of a Conference Held in Halifax, 1-3 May 1978, Geological Survey of Canada, 111-121.
[2]  Grilli, S.T., Subramanya, R., Svendsen, I.A. and Veeramony, J. (1994) Shoaling of Solitary Waves on Plane Beaches. Journal of Waterway, Port, Coastal, and Ocean Engineering, 120, 609-628.
[3]  Hsiao, S.C., Hsu, T.W., Lin, T.C. and Chang, Y.H. (2008) On the Evolution and Run-Up of Breaking Solitary Waves on a Mild Sloping Beach. Coastal Engineering, 55, 975-988.
[4]  Suhayda, J.N. and Pettigrew, N.R. (1977) Observations of Wave Height and Wave Celerity in the Surf Zone. Journal of Geophysical Research, 82, 1419-1424.
[5]  Stansell, P. and MacFarlane, C. (2002) Experimental Investigation of Wave Breaking Criteria Based on Wave Phase Speeds. Journal of Physical Oceanography, 32, 1269-1283.<1269:EIOWBC>2.0.CO;2
[6]  Yoo, J., Fritz, H.M., Haas, K.A., Work, P.A., Barnes, C.F. and Cho, Y. (2008) Observation of Wave Celerity Evolution in the Near Shore Using Digital Video Imagery. American Geophysical Union, Fall Meeting 2008, Abstract No. OS13D-1224.
[7]  Lippmann, T.C. and Holman, R.A. (1991) Phase Speed and Angle of Breaking Waves Measured with Video Techniques. In: N. Kraus, Ed., Coastal Sediments, ‘91, American Society of Civil engineers (ASCE), New York, 542-556.
[8]  Tissier, M., Bonneton, P., Almar, R., Castelle, B., Bonneton, N. and Nahon, A. (2011) Field Measurements and Non-Linear Prediction of Wave Celerity in the Surf Zone. European Journal of Mechanics, B Fluids, 30, 635-641.
[9]  Kimmoun, O. and Branger, H. (2007) A Particle Image Velocimetry Investigation on Laboratory Surf-Zone Breaking Waves over a Sloping Beach. Journal of Fluid Mechanics, 588, 353-397.
[10]  Sorensen, R.M. (1997) Basic Coastal Engineering. 2nd Edition, Springer-Science + Business Media, B.V.
[11]  Dean, R.G. and Darlymple, R.A. (2000) Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering 2, World Scientific Publishing Co., Singapore.
[12]  Stive, M.J.F. (1984) Energy Dissipation in Waves Breaking on a Gentle Slope. Coastal Engineering, 8, 99-127.
[13]  Sou, I.M. and Yeh, H. (2011) Laboratory Study of the Cross-Shore Flow Structure in the Surf and Swash Zones. Journal of Geophysical Research, 116, C03002.
[14]  Govender, K., Mocke, G.P. and Alport, M.J. (2004) Dissipation of Isotropic Turbulence and Length-Scale Measurements through the Wave Roller in Laboratory Spilling Waves. Journal of Geophysical Research, 109, C08018.
[16]  Abolhassani, M.D., Norouzy, A., Takavar, A. and Ghanaati, H. (2007) Noninvasive Temperature Estimation using Sonographic Digital Images. Journal of Ultrasound in Medicine, 26, 215-222.
[17]  Huang, H., Dabiri, D. and Gharib, M. (1997) On Errors of Digital Particle Image Velocimetry. Measurement Science and Technology, 8, 1427-1440.
[18]  Willert, C.E. and Gharib, M. (1991) Digital Particle Image Velocimetry. Experiments in Fluids, 10, 181-193.
[19]  Prieto, C.A. (2007) Velocities from Cross-Correlation: A Guide to Self-Improvement. The Astronomical Journal, 134, 1843-1848.
[20]  Govender, K., Mocke, G.P. and Alport, M. (2002) Video-Imaged Surf Zone Wave and Roller Structures and Flow Fields. Journal of Geophysical Research, 107, 3072-3083.
[21]  Oppenheim, A.V. and Schafer, R.W. (1975) Digital Signal Processing. Prentice-Hall, Upper Saddle River.
[22]  Thornton, E.B. and Guza, R.T. (1982) Energy Saturation and Phase Speeds Measured on a Natural Beach. Journal of Geophysical Research, 87, 9499-9508.
[23]  Postacchini, M. and Brocchini, M. (2014) A Wave-by-Wave Analysis for the Evaluation of the Breaking-Wave Celerity. Applied Ocean Research, 46, 15-27.


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