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Nonlinear Schrödinger invariants and wave statistics
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Image of FIG. 1.
FIG. 1.

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 .

Image of FIG. 2.
FIG. 2.

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.

Image of FIG. 3.
FIG. 3.

Free wave : the spatial variations of , its lower and upper bounds and (points), all representing the average values of five experiments.

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

Excess of kurtosis of (points) compared with the NLS theory from Eq. (17) (continuous curve) based on and at the wave maker.

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

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.


Generic image for table
Table I.

: principal spectral parameters.

Generic image for table
Table II.

: nontrivial cumulants , and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear Schrödinger invariants and wave statistics