JAMES KAIHATU, DEIRDRE DEVERY, RICHARD IRWIN AND JOHN GOERTZ COASTAL AND OCEAN ENGINEERING DIVISION ZACHRY DEPARTMENT OF CIVIL ENGINEERING TEXAS A&M UNIVERSITY.

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JAMES KAIHATU, DEIRDRE DEVERY, RICHARD IRWIN AND JOHN GOERTZ COASTAL AND OCEAN ENGINEERING DIVISION ZACHRY DEPARTMENT OF CIVIL ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TX, USA The Interaction Between Short Ocean Swell and Transient Long Waves – An Experimental Study

Outline Short wave-long wave interaction Experiments Dissipation analysis  Dissipation coefficient vs. spectral shape  Energy flux estimates  Wavelet transforms  Breaking Parameter Wavelet bicoherence Conclusions Future Work

Introduction How does the coexistence of transient long waves and short waves affect the overall dissipation characteristics of the wavefield? Are there significant interactions between short waves and transient long waves?

Experiments One year project from NEES program, National Science Foundation Use NEES Tsunami facility at Oregon State University Tsunami Wave Basin: 48.8m x 26.5m x 2.1m 29-paddle multi-directional piston wavemaker 4 resistance gages and 2 ADVs on movable bridge

Experiments Test No. Hs (cm) Tp (s)kh  =a/h UrUr Tsunami “height” ~30 cm Water depth 0.75 m Different runs with tsunami either at middle or end of swell

Long Wave Breaking Location With swell Without swell x=25.3m

Breaking Location Maximum free surface elevation

Dissipation Analysis Truncated time series: 2048 points

Dissipation Analysis From Kaihatu and Kirby (1996) Eddy viscosity breaking mechanism of Zelt (1991) (altered to operate on  ) where: Breaking Parameter (B.P.) - Solitary Wave Breaking!

Dissipation Analysis *: slope of log  ; o: neg. slope of log S(f) From Kaihatu et al. (2007 JGR) Linear shoaling and dissipation  n ~f 2 Random wave Bowen and Kirby Case A Random wave Bowen and Kirby Case B Random wave Bowen and Kirby Case C

Dissipation Analysis fp 0.5f(Nyq) Kaihatu et al. (2007)

Dissipation Analysis

B.P.=0.3 (Zelt 1991)

Dissipation Analysis Wavelet Transforms Average spectra over time of tsunami Calculate disspation quantities using averaged spectrum Swell 1 Swell 4 Tsunami-Swell 1 Tsunami-Swell 4 m=2 Spectra from Wavelet Transform Time Series of  S(f) α(f)

Dissipation Analysis B.P.=0.9 (Goertz et al., this conference)

Wavelet Bicoherence Swell 1 h=0.1m Tsunami and Swell 1 h=0.1m Wavelet bicoherence analysis using Dong et al. (2008) Thanks to Dr. Yuxiang Ma, Dalian Univ., for the analysis code

Conclusions Experiments on short wave interaction with a long transient wave performed. Dissipation characteristics of overall wavefield deduced using an assumed eddy viscosity breaking model. Spectral characteristics of dissipation of long wave – short wave combined signal are similar to that of short wave signal only. Energy flux estimates comparable between swell-alone and combined cases. Wavelet transforms offer different interpretation. Wave breaking parameter changes swell dissipation estimates. Wavelet bicoherence offers close examination of interactions.

Future Work Make further use of transient analyses  Wavelet transforms  Wavelet bicoherence (Dong et al. 2008)  Hilbert-Huang transforms (Huang et al. 1998)

Phase Speed Analysis Long wave breaking

Dissipation Analysis Dissipation coefficient  n nn nn h=0.2857mh=0.2429mh=0.1571m h=0.0714mh=0.0286mh=0.0029m Dissipation Coefficient Deduced from Wave Group Experiment of van Noorloos (2003) Kaihatu and El Safty 2011 (2010 ICCE) A1 A3 SS SS f f

Dissipation Analysis Dissipation Intensity = Total Dissipation / Length of time series Tsunami alone vs. Tsunami / SwellSwell alone vs. Tsunami / Swell