4.2 Wind Wave Energy Input
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Now the following equation connecting the resistance coefficient C10 with
the wind mean speed U10 and the non-dimensional frequency of the spectral
maximum iTmax normalized by the value Uw can be obtained for the air flow
case of neutral stratification:
~ ln Cz + "'C; 1 / 2 = ln ("' zJ;) -lniTmax,
where z =10m; and Cz = u; jU 2 (z) is the resistance coefficient.
(4.38)
Chalikov-Makin model of wind wave energy input.
The most
accurate numerical model of the statistical structure of the near-water
wave boundary layer based on the numerical solution of the Reynolds twodimensional equations is described by Chalikov (1986); Burgers & Makin
(1992); Chalikov & Belevich (1995); Belevich & Neelov (1998,2000). It is shown
that the wind wave energy input term Gin ( O", (3) can be expressed in the following form:
Gin(0",(3) = BuO"S(0",(3),
(4.39a)
where Bu is a non-dimensional wind wave interaction parameter. Its value
can be approximated as:
-ala-;- a2,
a3iTa(a4iTa- a5)- a6,
10 4 Bu = (a4iTa- a5)iTa,
a7iTa -as,
ag(iTa- 1) 2 + aw,
Ua :S: -1;
-1 Dt/2 < iT a < Dt ;
Dt fl2 (4.39b)
where iTa = (O"U>..f g) cos(f3-f3u) is the non-dimensional "apparent" frequency
of the wave propagating at the angle (3; f3u is the wind direction; and U>-.
is the wind speed at the height equal to the "apparent" wavelength Aa =
2ng / 0" 2 lcos((3- f3u) 1- The parameters a1 - aw and Dt, D2 are dependent on
the resistance coefficient C;>.. at the level z = Aa as follows:
D1 = 1.075 + 75C>-.;
a 1 = 0.25 + 3950>-.;
a3 = (ao- a2- at)/(ao- a4 + a5);
a5 = a4 Dt;
D2 = 1.2 + 3000>-.;
a2 = 0.35 + 150C>-.;
a4 = 0.30 + 3000>-.;
a5 = ao(1 - a3) ;
a7 = (ag(D2- 1) 2 + aw)/(D2- Dt);
as= a7 D1;
a9 = 0.35 + 240 C;>..;
a10 = -0.05 + 470 C>-.;
ao = 0.25aVa4.
( 4.40)
The parameter Bu has been thoroughly studied by Chalikov & Belevich
(1995). There are three main differences of this parameterization from Snyder's empirical relation. Firstly, the value of the function ( 4.39) becomes