A laboratory study of wave crest statistics and the role of directional spreading by M. Latheef, and C. Swan Proceedings A Volume 469(2152): April 8, 2013 ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society

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: ©2013 by The Royal Society