138
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
three or more hours. This traditional approach does not take into account
"sub-grid" effects, i.e. describing finer details of the wind wave field evolution.
That is why the solution is an averaging over these spatial-temporal steps.
The wave energy balance equation is assumed to describe sufficiently slow
wave field variations, since uniform and steady state wave processes are suggested in the derivation of the kinetic equation. In reality, it is necessary
to use a more complex equation relative to a fourth-order corrector for the
non-uniform wave field (Yuen&Lake, 1987). Only in the case of a spatially
uniform field can the traditional kinetic equation be applied.
In order to simplify the solution of the problem concerning wind wave
modelling, the wave field non-uniformity is taken into account only in the
advective term of the kinetic equation. The physical mechanisms forming the
wave energy spectrum are considered to be local and appear in the right-hand
side of the equation.
In this respect a question arises as to what extent such a solution is
correct. Two aspects of the problem can be considered. The first one is an
estimation of the error due to the discrete spatial and temporal wind field
description; the second is the problem of the correct description of physical
effects in the wind field under the given conditions.
It should be noted that the problem of obtaining sufficiently detailed
spatial and temporal wind field data is connected with general problems of
meteorology. This depends both on the state of this science and on the quality
of the current synoptic data. The information is collected by satellites, vessels
and synoptic stations. Nowadays meteorological centres produce wind field
calculations and forecasting, using numerical models of global atmospheric
circulation. The observation data is used as initial conditions to solve this
problem.
There are a number of specific questions in this respect. For example, how
to take into account the mesoscale wind speed changes such as wind gusts
and squalls? What is the influence of atmospheric boundary layer stratification? How can these circumstances influence the accuracy of surface wind
wave estimations? How can mesoscale effects be parameterized in wind wave
models?
Two of these problems will be considered in this section. An attempt
is undertaken to calculate the gust influence on the wind wave energy input
and to estimate mesoscale wave parameter oscillations on long-term spectrum
evolution.
Influence of gusts on the wind wave energy input. In order to estimate the influence of gusts on wind wave development, the parameterization
of the wind wave energy supply mechanism (Miles 1957, 1960; Snyder et al.,
1981) can be used. This theory can also be extended to the case when the
mean wind speed profile is a slowly changing function of time (Komen et al.,
1994). We consider how the wind field fluctuations can influence the wind
wave energy input.
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
three or more hours. This traditional approach does not take into account
"sub-grid" effects, i.e. describing finer details of the wind wave field evolution.
That is why the solution is an averaging over these spatial-temporal steps.
The wave energy balance equation is assumed to describe sufficiently slow
wave field variations, since uniform and steady state wave processes are suggested in the derivation of the kinetic equation. In reality, it is necessary
to use a more complex equation relative to a fourth-order corrector for the
non-uniform wave field (Yuen&Lake, 1987). Only in the case of a spatially
uniform field can the traditional kinetic equation be applied.
In order to simplify the solution of the problem concerning wind wave
modelling, the wave field non-uniformity is taken into account only in the
advective term of the kinetic equation. The physical mechanisms forming the
wave energy spectrum are considered to be local and appear in the right-hand
side of the equation.
In this respect a question arises as to what extent such a solution is
correct. Two aspects of the problem can be considered. The first one is an
estimation of the error due to the discrete spatial and temporal wind field
description; the second is the problem of the correct description of physical
effects in the wind field under the given conditions.
It should be noted that the problem of obtaining sufficiently detailed
spatial and temporal wind field data is connected with general problems of
meteorology. This depends both on the state of this science and on the quality
of the current synoptic data. The information is collected by satellites, vessels
and synoptic stations. Nowadays meteorological centres produce wind field
calculations and forecasting, using numerical models of global atmospheric
circulation. The observation data is used as initial conditions to solve this
problem.
There are a number of specific questions in this respect. For example, how
to take into account the mesoscale wind speed changes such as wind gusts
and squalls? What is the influence of atmospheric boundary layer stratification? How can these circumstances influence the accuracy of surface wind
wave estimations? How can mesoscale effects be parameterized in wind wave
models?
Two of these problems will be considered in this section. An attempt
is undertaken to calculate the gust influence on the wind wave energy input
and to estimate mesoscale wave parameter oscillations on long-term spectrum
evolution.
Influence of gusts on the wind wave energy input. In order to estimate the influence of gusts on wind wave development, the parameterization
of the wind wave energy supply mechanism (Miles 1957, 1960; Snyder et al.,
1981) can be used. This theory can also be extended to the case when the
mean wind speed profile is a slowly changing function of time (Komen et al.,
1994). We consider how the wind field fluctuations can influence the wind
wave energy input.