A segment of the full surface elevation observed at (gauge 8), the corresponding free wave , and the second and third-order corrections ( and ) removed from to obtain .
Spatial variations of the averaged Hamiltonian , wave action and momentum . Each point represents an overall average of five experimental series with the range of values observed in separate series indicated by vertical lines (not clearly visible for ). The horizontal straight lines correspond to the expected theoretical values along the channel in accord to the NLS model.
Free wave : the spatial variations of , its lower and upper bounds and (points), all representing the average values of five experiments.
Average spectra of the actual series observed at (a) (gauge 1), (b) (gauge 5), and (c) (gauge 8) from the wave maker. Similarly, the spectra of the corresponding free-wave series observed at (d) , (e) , and (f) from the wave maker.
Excess of kurtosis of (points) compared with the NLS theory from Eq. (17) (continuous curve) based on and at the wave maker.
Exceedance distributions observed at (a) (gauge 1), (b) (gauge 5), and (c) (gauge 8) from the wave maker, describing wave heights (points), crests (hollow triangles) and trough amplitudes (solid triangles) compared with the predictions from of Eq. (18) for wave crest and trough amplitudes, and of Eq. (22) for wave heights. Gaussian limits (dashed curves) are represented by of Eq. (20) for linear crest and trough amplitudes and of Eq. (21) for wave heights.
Same as Fig. 6(c) except for observed at (gauge 8) from the wave maker, reproduced from the work of Cherneva et al. (Ref. 21). In this case, the theoretical distributions for wave heights, for wave crests, and for trough amplitudes follow from the expressions given in Eqs. (8), (11), and (12) of the same reference.
: principal spectral parameters.
: nontrivial cumulants , and .
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