Chapter 1: INTRODUCTION
where
,
K Z -
)
is the frequency-direction spectrum of the surface waves. A
formulation due to Donelan and Pierson (1987) relates w
E at each frequency
to the wind speed as
/
/
cos
cos
0.194
1
1
( )
w
a
k
k
U
U
c k
c k
S
S
E
U
-
-
Z
U
§
·
¨
¸
¨
¸
©
¹
,
(1.126)
where
/ k
U S
is the wind speed at the height of one half wavelength
( /2
/k
O
S ), which is taken as the relevant forcing parameter for a
component of wavenumber, k, and phase speed, c(k).
Terray et al. (1996) introduced an effective phase speed, c , related to
wind input by parameterizing 0
F in terms of this speed and the wind stress
0
W as:
2
0
0 /
F c
cu
W U
|
,
(1.127)
53
Figure 1-15. The ratio of the effective phase speed to the phase speed of the wind wave
spectral peak, / p
c c , versus inverse wave age,
/
a
p
u c
. Reproduced from Terray et al. (1996)
with the permission of American Meteorological Society.