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Interactions between Surface Swell and Tsunamis – A First Look

Interactions between Surface Swell and Tsunamis – A First Look. Hoda El Safty and James M. Kaihatu Zachry Department of Civil Engineering Texas A&M University College Station, TX, USA. Motivation. 2004 Indian Ocean Tsunami from Koh Jum Island. Motivation.

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Interactions between Surface Swell and Tsunamis – A First Look

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  1. Interactions between Surface Swell and Tsunamis – A First Look Hoda El Safty and James M. Kaihatu Zachry Department of Civil Engineering Texas A&M University College Station, TX, USA IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  2. Motivation 2004 Indian Ocean Tsunami from KohJum Island IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  3. Motivation • Generally – default paradigm for tsunamis: solitary wave • Used for lab studies of tsunami damage • Madsen et al. (2008) • Solitary wave paradigm flawed • Cause order of magnitude errors in spatial and temporal evolution over a sloping bottom IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  4. Interaction with the Swell Wave Field • Hypothesis: • Overlying swell wavefield can have some subtle effect on underlying tsunami • Front face steepness • Wave-wave interaction • Run long wave through random swell field • Use transient analysis (wavelet, Hilbert-Huang) to investigate effects IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  5. NEES Payload • 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 IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  6. Test Conditions Gage 1 Gage 8 Gage 16 Gage 20 Tsunami “height” ~30 cm Water depth 0.75 m Different runs with tsunami either in middle or end of swell record IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  7. Experiments Tsunami Only Tsunami with Swell IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  8. Analysis • Maximum Surface Elevation • As proxy for waveheight: maximum surface elevation in record • Maximum surface elevation reached earlier with combined conditions than with either alone. • Different results with tsunami in middle or at end of swell record. Blue: Tsunami Black: Swell Red: Combined Tsunami at End Blue: Tsunami Black: Swell Red: Combined Without Swell With Swell Tsunami in Middle IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  9. Wavelet Analysis • Morlet Wavelet Transform • Data from experiment – periodic signal interacting with a transient signal • Standard Fourier Transform techniques not suitable • Wavelet transform – time-dependent frequencies • Spectral densities as a function of frequency and time The Morlet Wavelet IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  10. Wavelet Analysis Gage 1 Gage 8 Gage 16 Gage 20 Tsunami Only IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  11. Wavelet Analysis Gage 1 Gage 8 Gage 16 Gage 20 Tsunami with Swell: Hs=5cm, Tp=2s IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  12. Wavelet Analysis Gage 1 Gage 8 Gage 16 Gage 20 Tsunami with Swell: Hs=5cm, Tp=4s IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  13. Wavelet Analysis Gage 1 Gage 8 Gage 20 Gage 16 Tsunami with Swell: Hs=10cm, Tp=2s IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  14. Wavelet Analysis Gage 8 Gage 1 Gage 16 Gage 20 Tsunami with Swell: Hs=10cm, Tp=4s IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  15. Hilbert-Huang Transform • Hilbert Transform plus Empirical Model Decomposition • Take original nonperiodic signal • Calculate envelope with Hilbert Transform, then calculate mean • Subtract mean from original signal • New signal • Do this on each updated signal k times • Result – mode c1 • Subtract mode c1 from original data – obtain new data • Perform sifting process again • Advantage: • No apriori basis function • Modes usually have some physical basis Top: Signal. Middle: Signal, envelope and mean of envelope. Bottom: Original signal and signal minus mean of envelope IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

  16. Conclusions and Future Work • It was hypothesized that the overlying swell field might have some effect on a long tsunami (front face steepness, etc.) • Experiments were run at the NEES Tsunami Facility at Oregon State University • Some indication of swell affecting maximum surface amplitude of overall wave field • Wavelet analysis: spectral structure of tsunami affected by swell • Hilbert-Huang Transform may help break motion up into physically relevant scales. IAHR Europe Meeting: 4-6 May 2010 Edinburgh UK

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