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Research Papers: Ocean Engineering

A Note on the Second-Order Contribution to Extreme Waves Generated During Hurricanes

[+] Author and Article Information
Mark L. McAllister

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: mark.mcallister@eng.ox.ac.uk

Thomas A. A. Adcock

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: thomas.adcock@eng.ox.ac.uk

Paul H. Taylor

Faculty of Engineering and Mathematical
Sciences,
University of Western Australia,
Crawley, WA 6009, Australia
e-mail: paul.taylor@eng.ox.ac.uk

Ton S. van den Bremer

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: ton.vandenbremer@eng.ox.ac.uk

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 26, 2018; final manuscript received January 11, 2019; published online February 21, 2019. Assoc. Editor: Puneet Agarwal.

J. Offshore Mech. Arct. Eng 141(4), 041102 (Feb 21, 2019) (7 pages) Paper No: OMAE-18-1163; doi: 10.1115/1.4042540 History: Received September 26, 2018; Revised January 11, 2019

High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behavior. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (2006, “Directional Spectra of Hurricane Wind Waves,” J. Geophys. Res. Oceans, 111(C8), epub). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are generally supported by experimental observations, but we note the difficulty of generating and focusing the high-frequency tail of the spectrum experimentally. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealized directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.

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Topics: Waves , Filtration
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References

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Figures

Grahic Jump Location
Fig. 1

Illustration of expected wave-averaged surface elevation under extreme waves generated during tropical storms. Panels ad show examples of directional spreading distributions D(f, θ) measured in each quadrant of a hurricane taken from Y06 (see Table 1 for full details); contours are drawn at 0.9, 0.8, 0.7, 0.6, and 0.5, and vertical lines show the direction local wind (solid) and dominant waves (dashed). Panels eh show the parameterization of spreading distributions above proposed in Sec. 2. Panels il show the linear NewWave free-surface elevation for each of the proposed directional distributions and a JONSWAP spectrum D(f,θ)η̂(f). Panels mp show the predicted wave-averaged surface elevation for each NewWave group: unfiltered (black lines) and low-pass filtered at 0.5fp (red lines, gray in print version). The right-hand side blue axes for rows il and mp illustrate our results at a field scale of 50:1 (a0 = 7.5 m, d =100 m, and f0 = 0.1 Hz), whereas the left-hand side axes correspond to lab scale (see Sec. 4).

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Fig. 2

Second-order difference interaction kernel B (from Ref. [11], see Appendix) shown as a function of normalized frequency f/fp and crossing angle θ1θ2 of interacting wave pairs for fp = 0.7 Hz and d =2.0 m

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Fig. 3

The effects of water depth on formation of setup and corresponding second-order contribution to overall crest height; predictions shown for water depths kd = 0.5, 1, 10 left to right and directional skew Δθ = 0–180 deg in 10 deg increments from black to gray. Panels ac show second-order difference waves; panels df show second-order sum waves; panels gi show total second-order contribution. Calculations are carried out for linear wave groups η(1) based on the parameters in Table 2.

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Fig. 4

Predicted amplitude of second-order contribution to crest height as a function of high-frequency cutoff for a JONSWAP spectrum with the parameters detailed in Table 2 and directional distribution (3) for Δθ = 0, 90, 180 deg

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Fig. 5

Schematic diagram, showing wave tank setup and measurement gauge locations

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Fig. 6

Results of laboratory experiments with frequency-dependent directional skew (2) for different directional skews Δθ = 90, 135, 180, 225 deg, and frequency-independent spreading σθ = 20 deg. Panels ad show input directional distributions D(f, θ) with contours drawn at 0.9, 0.8, 0.7, 0.6, and 0.5. Panels ef show the linear free surface elevation η(1) and panels ij show second-order difference waves, where experiments are shown as black lines and predictions based on inputs to the tank are shown as red lines (gray in print version).

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