THE NEAR-SURFACE LAYER OF THE OCEAN
3
/ a
z u
H
N H
I ]
,
(1.151)
where
/
a
a
T
w
u
N
c c
4
, a
u is the friction velocity (in air), His the
dissipation rate of turbulent kinetic energy, stability parameter ] is defined
in (1.41) and u and w are the horizontal and vertical components of wind
velocity vector, respectively. The stability parameter is negative when the
atmosphere is statically unstable and positive when it is statically stable. In
order to make this criterion applicable to both atmosphere and ocean, in the
definition of the stability parameter we have replaced z with z .
For intermediate depths, the constant stress and heat flux assumptions
(that the Monin-Oboukhov theory is based on) strictly speaking are no
longer valid (also because of volume sources). The Monin-Oboukhov theory,
however, often holds even in the case of vertically variable fluxes. An
approach to modifying the Oboukhov length scale L O in order to account for
the presence of volume sources is considered in Chapter 4.
A commonly used approximation for the universal functions I and I T ,
based on the Kansas experiment is as follows (Kraus and Businger, 1994):
1/ 4
1/ 3
1
for 0
1
for -0.20
0
1.26 8.38
for
0.20
M
E]
]
I
D ]
]
]
]
d
­
° °
|
d
®
°
° ¯
,
(1.152)
1/ 2
1/ 3
1
for 0
1
for -1.0
0
28.26 98.96
for
1.0
T
E]
]
I
D ]
]
]
]
d
­
° °
|
d
®
°
° ¯
(1.153)
where E = 5, and D = 16. For the dissipation rate of turbulent kinetic energy
(TKE), Wyngaard et al. (1971) proposed:
3/ 2
2 / 3
3/ 2
2 / 3
1 0.5
, for
0
1 2.5
, for
0
H
]
]
I ]
]
]
­
°
®
°
t
¯
(1.154)
60
M