4.3 Wave Energy Dissipation in Deep Water
131
ofthe spectral maximum a max; the parameter n, characterizing the spectrum
sharpness, and ap is the low-frequency limitation of the spectral equilibrium
area. All these parameters were obtained earlier using field data as functions
of the stage of wind sea development. The value iTmax is the dimensionless
frequency of the spectral maximum (Davidan, 1969; Davidan et al., 1978). At
each stage of wind sea development these parameters are connected with the
non-dimensional frequency of the main spectral maximum iTmax = U10amax/g
as follows:
n = 5exp (0.5iTmax- 0.4) 2
when iTmax < 2.4
( 4.48)
m (a ) = 1 27. 10-3 g-2u4o--3.19
0 1r
•
max
As can be seen from adduced relations, actually it is enough to have
a spectral maximum frequency and wind velocity in order to calculate the
wave frequency spectrum. The peculiarity of the frequency spectrum ( 4.4 7) is
the second maximum with its decreasing relative value, its location displacement relative to the spectral maximum is shifted to the higher frequency
area.
Davidan passed from normalized spectral parameters with respect to U10
(wind velocity at 10 m height) to their normalization by the dynamic velocity U. in order to make the approximation (4.48) more universal. On the
basis of the data (Davidan et al., 1985), the other parameters of the wind
wave spectrum are defined by transition from ulO to u.:
*
* -0.39 (
*0.25)
a max = 0.5 mo
th 0.52mo
*
*
h0.28 (
3 .3.21)
atr = amaxct
3.72 ·10 amax
( 4.49)
ap = 1.1 a max ;
n=8.0+3.0 th 0 · 75 {J [1.2·10 4 (a~ax-0.09)]J} sign(a*-0.09).
The spectral approximation (4.46) allows the analysis of the formation of
wind wave spectral structure in different frequency bands.
Correlation of physical mechanisms with spectrum approximation.
One of the most interesting features of the LB SOIN spectrum is its frequency
structure based on detailed analysis of field observations. In particularly, the
second maximum at frequencies greater than the peak spectrum frequency as
well as the transition to the equilibrium state approximation is evidence of
131
ofthe spectral maximum a max; the parameter n, characterizing the spectrum
sharpness, and ap is the low-frequency limitation of the spectral equilibrium
area. All these parameters were obtained earlier using field data as functions
of the stage of wind sea development. The value iTmax is the dimensionless
frequency of the spectral maximum (Davidan, 1969; Davidan et al., 1978). At
each stage of wind sea development these parameters are connected with the
non-dimensional frequency of the main spectral maximum iTmax = U10amax/g
as follows:
n = 5exp (0.5iTmax- 0.4) 2
when iTmax < 2.4
( 4.48)
m (a ) = 1 27. 10-3 g-2u4o--3.19
0 1r
•
max
As can be seen from adduced relations, actually it is enough to have
a spectral maximum frequency and wind velocity in order to calculate the
wave frequency spectrum. The peculiarity of the frequency spectrum ( 4.4 7) is
the second maximum with its decreasing relative value, its location displacement relative to the spectral maximum is shifted to the higher frequency
area.
Davidan passed from normalized spectral parameters with respect to U10
(wind velocity at 10 m height) to their normalization by the dynamic velocity U. in order to make the approximation (4.48) more universal. On the
basis of the data (Davidan et al., 1985), the other parameters of the wind
wave spectrum are defined by transition from ulO to u.:
*
* -0.39 (
*0.25)
a max = 0.5 mo
th 0.52mo
*
*
h0.28 (
3 .3.21)
atr = amaxct
3.72 ·10 amax
( 4.49)
ap = 1.1 a max ;
n=8.0+3.0 th 0 · 75 {J [1.2·10 4 (a~ax-0.09)]J} sign(a*-0.09).
The spectral approximation (4.46) allows the analysis of the formation of
wind wave spectral structure in different frequency bands.
Correlation of physical mechanisms with spectrum approximation.
One of the most interesting features of the LB SOIN spectrum is its frequency
structure based on detailed analysis of field observations. In particularly, the
second maximum at frequencies greater than the peak spectrum frequency as
well as the transition to the equilibrium state approximation is evidence of