4.4 Influence of Mesoscale Effects on Wind Wave Evolution
141
Effect of wind wave paraiileter quasi-oscillation on the non-linear
spectrum evolution.
For several decades temporal wave records with
about 20-minute duration were obtained in most wind wave measurements
under field conditions. Records of duration were believed to be sufficient to
obtain a representative estimation of the wave energy spectral density. The
process was considered to be ergodic in the sense that the probabilistic characteristics of some records were assigned a known degree of similarity with
the probabilistic characteristics of the hypothetical (obtained under analogous conditions) ensemble of selected functions. Such temporal intervals were
called "quasi-stationary intervals" (Davidan et al., 1985). It was assumed that
the local wave energy, defined as E = ('f/ 2 ) = J S(k) dk, remained constant,
i.e. E = ('f/ 2 ) = const (where 'fJ = rJ(r, t) was the sea surface displacement,
which was a function of the spatial coordinate r and time t, S was the spatial wind wave spectrum). Deviation from this condition was explained as
sampling variability of the random process.
However, the assumption of the existence of "quasi-stationary intervals"
became doubtful due to studies made in the last decade. The latest data reveal
that the condition of constant process dispersion is not valid for the quasistationary interval. The local dispersion creates a quasi-periodic fluctuation
(or simply quasi-oscillations) in both the temporal (T3) and the corresponding
spatial scale range. This phenomenon, well known as SMIWEH (Smoothed Instantaneous Wave Energy History), was described by Zaslavskii&Krasitskii
(1993), Bitner-Gregersen & Gran (1983), Mase (1989), and Sand (1982).
Measurements of the local wave dispersion E = ('f/ 2 ) obtained by Zaslavskii and Krasitskii (1993) in the North Atlantic served as experimental
evidence of the existence of these effects. The experiment was performed under stationary conditions of wave development and in the absence of swell.
The variation of the local dispersion E(t), obtained by a running averaging
method with a 60s interval, is shown in Fig. 4.22a.
Fluctuations of the wave dispersion E (t) = E + E 1 (t) with an approximately 5 minute temporal scale can be seen. The amplitude E 1 (t) comparable
with E dispersion is estimated for the total record. These fluctuations are not
dependent on the group structure of the wind waves estimated by a narrow
band of their spectrum. The average wave period is equal to 6 s, whereas the
temporal wave group scale is less than 60 s. It is important to note that the
sampling variability estimates are smaller than the wave dispersion calculations.
Some other papers contain similar data. An example of time variation of
wave dispersion (Andreyev, 1988) is presented in Fig. 4.22b. The dispersion
is estimated for 150 s intervals with a fluctuation period of 7-15 minutes.
Similar data for the variation E(t) with 300 s averaging were obtained by
Yefimov & Soloviev (1984). They estimated a 15-20 min fluctuation period.
The local wind wave dispersion fluctuation is connected with variations
of the corresponding wave spectra. Such spectral density fluctuations of the
141
Effect of wind wave paraiileter quasi-oscillation on the non-linear
spectrum evolution.
For several decades temporal wave records with
about 20-minute duration were obtained in most wind wave measurements
under field conditions. Records of duration were believed to be sufficient to
obtain a representative estimation of the wave energy spectral density. The
process was considered to be ergodic in the sense that the probabilistic characteristics of some records were assigned a known degree of similarity with
the probabilistic characteristics of the hypothetical (obtained under analogous conditions) ensemble of selected functions. Such temporal intervals were
called "quasi-stationary intervals" (Davidan et al., 1985). It was assumed that
the local wave energy, defined as E = ('f/ 2 ) = J S(k) dk, remained constant,
i.e. E = ('f/ 2 ) = const (where 'fJ = rJ(r, t) was the sea surface displacement,
which was a function of the spatial coordinate r and time t, S was the spatial wind wave spectrum). Deviation from this condition was explained as
sampling variability of the random process.
However, the assumption of the existence of "quasi-stationary intervals"
became doubtful due to studies made in the last decade. The latest data reveal
that the condition of constant process dispersion is not valid for the quasistationary interval. The local dispersion creates a quasi-periodic fluctuation
(or simply quasi-oscillations) in both the temporal (T3) and the corresponding
spatial scale range. This phenomenon, well known as SMIWEH (Smoothed Instantaneous Wave Energy History), was described by Zaslavskii&Krasitskii
(1993), Bitner-Gregersen & Gran (1983), Mase (1989), and Sand (1982).
Measurements of the local wave dispersion E = ('f/ 2 ) obtained by Zaslavskii and Krasitskii (1993) in the North Atlantic served as experimental
evidence of the existence of these effects. The experiment was performed under stationary conditions of wave development and in the absence of swell.
The variation of the local dispersion E(t), obtained by a running averaging
method with a 60s interval, is shown in Fig. 4.22a.
Fluctuations of the wave dispersion E (t) = E + E 1 (t) with an approximately 5 minute temporal scale can be seen. The amplitude E 1 (t) comparable
with E dispersion is estimated for the total record. These fluctuations are not
dependent on the group structure of the wind waves estimated by a narrow
band of their spectrum. The average wave period is equal to 6 s, whereas the
temporal wave group scale is less than 60 s. It is important to note that the
sampling variability estimates are smaller than the wave dispersion calculations.
Some other papers contain similar data. An example of time variation of
wave dispersion (Andreyev, 1988) is presented in Fig. 4.22b. The dispersion
is estimated for 150 s intervals with a fluctuation period of 7-15 minutes.
Similar data for the variation E(t) with 300 s averaging were obtained by
Yefimov & Soloviev (1984). They estimated a 15-20 min fluctuation period.
The local wind wave dispersion fluctuation is connected with variations
of the corresponding wave spectra. Such spectral density fluctuations of the