THE NEAR-SURFACE LAYER OF THE OCEAN
1/ 3
1/ 4
, for
1
, for 0
1
/
, for 0
s
s
s
sb
s
cr
cr
u z a c Ri
Ri Ri
K
uz
Ri
Ri Ri
u z
Ri Ri
Ri Ri
N
N
D
N
­
° °
! t
®
°
d
° ¯
(3.106)
where dimensionless constants Ri m = -0.20, R is = -1.0, Ri cr = 0.25, D = 16, a m
= 1.26, a s = -28.86, c m = 8.38, and c s = 98.96 are derived from atmospheric
measurements (see Chapter 1, section 1.7.2).
The first two lines in (3.105) and (3.106) are the boundary layer
parameterization for the unstably stratified mixed layer; the third line is the
boundary layer parameterization for the stably stratified mixed layer (which
is similar to (3.97)).
In order to ensure a smooth transition from the mixed layer to the
thermocline, the eddy mixing coefficient for momentum is finally defined as
,
max(
)
M
M b
M t
K
K K
(3.107)
where Mb
K and Mt
K are the mixing coefficients for momentum in the mixed
layer and thermocline respectively. The mixing coefficient for scalar
property s is defined in the similar way:
max
,
s
sb
st
K
K K ,
(3.108)
where sb
K and st
K are the mixing coefficients for scalar properties in the
mixed layer and thermocline respectively. Furthermore, under the
assumption that the turbulent Prandtl number is equal to unity in
thermocline,
st
M t
K
K .
(3.109)
To take into account the free convection above a stratified layer, u in
(3.105) and (3.106) can be replaced by
1/ 2
2
2
u
w
, where w is the
Priestly (1959) convective velocity scale (3.95).
Figure 3-28 compares parameterization (3.107) with the mixing
coefficient for momentum that is derived from the R/V Moana Wave
COARE IOP leg 2 turbulence data of Moum and Caldwell (1994) and Smyth
et al. (1996). The mixing coefficient in the thermocline Mt
K entering (3.107)
is parameterized with equation (3.103). The vertical mixing coefficient for
momentum is calculated using the “dissipation method” as in Peters et al.
(1988):
212