a laboratory study of wave crest statistics and the role of directional spreading by m. latheef, and...
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![Page 1: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/1.jpg)
A laboratory study of wave crest statistics and the role of directional spreading
by M. Latheef, and C. Swan
Proceedings AVolume 469(2152):20120696
April 8, 2013
©2013 by The Royal Society
![Page 2: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/2.jpg)
Field data describing the normalized crest-height distribution, ηc/Hs, based upon a reanalysis of the field observations reported in Christou & Ewans [14] for all storms with Hs≥12 m.
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 3: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/3.jpg)
Schematic of the wave basin showing the layout of the wave gauges: (a) plan view and (b) side elevation.
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 4: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/4.jpg)
Preliminary measurements of a focused wave group: (a) η(t) at the focus position; (b) η(y) at the instant of wave focusing (y is transverse to the mean wave direction) and (c) the amplitude
spectrum, an(ω).
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 5: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/5.jpg)
Energy spectra, Sηη(ω), for the two sea states: (a) Tp=1.6 s, Hs=0.10 m and σθ=15° and (b) Tp=1.6 s, Hs=0.20 m and σθ=15°, based on data recorded at (black solid line) gauge 1, (black
dashed line) gauge 4 and (black dotted line) gauge 7 with comparisons to ...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 6: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/6.jpg)
Quantification of the DSF, comparisons between (dots) data from the maximum-likelihood method (MLM) and (grey solid line) the theoretical spreading function for the sea state Tp=1.6 s,
Hs=0.08 m with (a) σθ=15° and (b) σθ=30°.
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 7: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/7.jpg)
Variability of the normalized crest height, ηc/Hs, for a sea state with Tp=1.6 s, Hs=0.10 m and σθ=15°: (a) (solid grey line) 20 (3 h) simulations and (black solid line) the amalgamated dataset;
(b) measured data recorded at (diamonds) gauge 1, (squares) ga...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 8: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/8.jpg)
Normalized crest heights, ηc/Hs, for uni-directional (σθ=0°) sea states (Tp=1.6 s, kpd=2.019) of varying steepness: (a) , (b) , (c) and (d) .
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 9: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/9.jpg)
Normalized crest heights, ηc/Hs, for directionally spread (σθ=15°) sea states (Tp=1.6 s, kpd=2.019) of varying steepness: (a) , (b) , (c) , (d) , (e) and (f) .
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 10: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/10.jpg)
Normalized crest heights, ηc/Hs, for directionally spread (σθ=30°) sea states (Tp=1.6 s, kpd=2.019) of varying steepness: (a) , (b) and (c) .
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 11: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/11.jpg)
Crest-height distributions normalized with respect to the Rayleigh distribution, ηc/ηL, for sea states (Tp=1.6 s, kpd=2.019) of varying steepness for: (a) σθ=0°, (b) σθ=15° and (c) σθ=30°;
experimental data ((solid line) , (dashed line) and (dotted line) )...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 12: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/12.jpg)
Crest-height distributions normalized with respect to the Rayleigh distribution, ηc/ηL, for: (a) varying Tp and steepness (Hs=0.15 m, σθ=15°, (black thick solid lines) Tp=1.6 s and , (black thick
dashed lines) Tp=1.4 s and , and (black thick dotted lines) T...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 13: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/13.jpg)
Crest-height distributions normalized with respect to the Rayleigh distribution, ηc/ηL, for sea states (Tp=1.6 s, kpd=2.019) with varying directional spreads ((black solid lines) σθ=0°, (black
dashed line) σθ=15° and (black dotted lines) σθ=30°), for: (a) ,...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 14: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/14.jpg)
The influence of directionality on: (a) the water surface elevation, η(x), obtained for (grey solid lines) σθ=0°, (black dashed lines) σθ=15° and (black solid lines) σθ=30° and (b) the normalized
steepness (black circles) ηck and (grey circles) ).
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society
![Page 15: A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152):20120696 April](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649cee5503460f949bca3b/html5/thumbnails/15.jpg)
Normalized crest-height distribution, ηc/ηL, for sea states (Tp= 1.6 s, ) with frequency-independent and frequency-dependent directional spreading: (black solid lines) σθ=15°, (black
dashed lines) [43] and (black dotted lines) σθ=30° compared with the Forri...
M. Latheef, and C. Swan Proc. R. Soc. A 2013;469:20120696
©2013 by The Royal Society