4.4 Influence of Mesoscale Effects on Wind Wave Evolution
137
wave group fluctuations range from tens to hundreds of seconds. The wave
groups repeat themselves approximately every 10-15 average wave periods
( 7 2 ~ 10-15 71), consisting of 5-9 waves. As a first approximation, the temporal scale of their frequency of occurrence can be assumed as 7 2 ~ 10 2 s.
The so-called "quasi-oscillations" can be referred to the third temporal
fluctuation scale of the sea surface. They are fairly well traced in changes of
the form of the frequency spectrum and in its parameters even under stable
wave development conditions (Andreyev 1988; Zaslavskii & Krasitskii, 1993;
Bitner-Gregersen& Gran, 1983). The quasi-oscillation periods are approximately equal to 5-20 min. The scale of these periods can be estimated as
7 3 ~ 10 3 s. A description of this phenomenon will be given later this chapter.
The wave field changes occurring within a period of 3-6 hours represent
the fourth temporal scale. This temporal scale is estimated as 7 3 ~ 10 4 s.
Significant changes in the wind wave spectrum and in all its parameters usually occur within this time interval. As far as the temporal scale is concerned
the surface wind field data with a similar temporal step are input to the
mathematical models for wind wave numerical simulations. The mathematical models used for practical application are based on the numerical solution
of the wave energy balance equation (Davidan et al., 1985; Komen et al.,
1994). The field changes occurring within smaller temporal and spatial scales
are not taken into account. In other words, the numerical results represent
estimations of the wave field calculated on the basis of the wind field averaged
over this time interval.
The problem is that these results are usually compared with the full-scale
measurements made over a shorter time interval, namely, within a quasistationary range. A question appears whether it is correct to compare the
random process parameter estimations averaged over different time intervals.
The next temporal scale of the wave wind field evolution is a synoptic
range order of 7 5 ~ 10 5 (Davidan et al., 1978). Numerical simulations of
wind waves in forecasting are usually carried out by means of mathematical
models for these time intervals. The scale variation of the wind wave field
(including seasonal, interannual variability, etc.) could be enlarged. But their
detailed consideration is beyond the scope of this study.
It is important to point out that all the aforementioned temporal scales
of wind wave field changes differ one from another by an order of magnitude.
This allows considering the wave field evolution at one scale irrespective of
the others. However, the problem of the influence of one scale of the spatialtemporal wave field evolution on the other still remains unstudied.
The problem of mesoscale effects in wind sea numerical simulations.
The wave energy balance equation (3.1) is used in modern methods of wind
wave numerical simulations. A grid with a specific spatial step is used to solve
the problem numerically. The wind speed data is introduced in the model with
a definite time interval. As a rule, the spatial step comprises tens or hundreds
of miles. The near-surface wind values are introduced with a time interval of
137
wave group fluctuations range from tens to hundreds of seconds. The wave
groups repeat themselves approximately every 10-15 average wave periods
( 7 2 ~ 10-15 71), consisting of 5-9 waves. As a first approximation, the temporal scale of their frequency of occurrence can be assumed as 7 2 ~ 10 2 s.
The so-called "quasi-oscillations" can be referred to the third temporal
fluctuation scale of the sea surface. They are fairly well traced in changes of
the form of the frequency spectrum and in its parameters even under stable
wave development conditions (Andreyev 1988; Zaslavskii & Krasitskii, 1993;
Bitner-Gregersen& Gran, 1983). The quasi-oscillation periods are approximately equal to 5-20 min. The scale of these periods can be estimated as
7 3 ~ 10 3 s. A description of this phenomenon will be given later this chapter.
The wave field changes occurring within a period of 3-6 hours represent
the fourth temporal scale. This temporal scale is estimated as 7 3 ~ 10 4 s.
Significant changes in the wind wave spectrum and in all its parameters usually occur within this time interval. As far as the temporal scale is concerned
the surface wind field data with a similar temporal step are input to the
mathematical models for wind wave numerical simulations. The mathematical models used for practical application are based on the numerical solution
of the wave energy balance equation (Davidan et al., 1985; Komen et al.,
1994). The field changes occurring within smaller temporal and spatial scales
are not taken into account. In other words, the numerical results represent
estimations of the wave field calculated on the basis of the wind field averaged
over this time interval.
The problem is that these results are usually compared with the full-scale
measurements made over a shorter time interval, namely, within a quasistationary range. A question appears whether it is correct to compare the
random process parameter estimations averaged over different time intervals.
The next temporal scale of the wave wind field evolution is a synoptic
range order of 7 5 ~ 10 5 (Davidan et al., 1978). Numerical simulations of
wind waves in forecasting are usually carried out by means of mathematical
models for these time intervals. The scale variation of the wind wave field
(including seasonal, interannual variability, etc.) could be enlarged. But their
detailed consideration is beyond the scope of this study.
It is important to point out that all the aforementioned temporal scales
of wind wave field changes differ one from another by an order of magnitude.
This allows considering the wave field evolution at one scale irrespective of
the others. However, the problem of the influence of one scale of the spatialtemporal wave field evolution on the other still remains unstudied.
The problem of mesoscale effects in wind sea numerical simulations.
The wave energy balance equation (3.1) is used in modern methods of wind
wave numerical simulations. A grid with a specific spatial step is used to solve
the problem numerically. The wind speed data is introduced in the model with
a definite time interval. As a rule, the spatial step comprises tens or hundreds
of miles. The near-surface wind values are introduced with a time interval of