The scaling used in parameterizations (3.105) and (3.106) is consistent
with the idea by Stommel (1960) that the shear within the mixed layer is
proportional to the friction velocity. For the vertical eddy viscosity, Ekman
(1905, cf. Santiago-Mandujano and Firing, 1990) proposed a
parameterization
2
*
~
M
K
u , which is not consistent with the logarithmic
layer asymptote observed for neutral stratification conditions in the mixed
layer. The analysis of Santiago-Mandujano and Firing (1990) shows that
Ekman’s parameterization
2
*
~
M
K
u appears as a result of assuming that the
mixed layer depth is proportional to the Ekman scale,
* /
E
L u f . Ekman’s
parameterization ignores any dependence of M
K on depth z.
The boundary layer parameterizations (3.105) and (3.106) results in
~
M
K
u , which is consistent with the logarithmic layer asymptote
M
K
u z
N . The parameterization of Large et al. (1994) based on boundary
layer scaling also implies that
~
M
K
u .
An important feature of turbulence that has to be taken into account in
mixing parameterization schemes is that it is a fundamentally nonlocal
process (Stull and Kraus, 1987; Large et al., 1994). This is because the
turbulent transport is performed via a cascade of eddies. The nonlocal
behavior of turbulence is associated with the presence of spatially coherent
organized motions. There are numerous observations of coherent structures
in the surface layer of the ocean, including Kelvin-Helmholtz billows
(Thorpe, 1969), Langmuir cells (Weller and Price, 1988; Thorpe et al.,
2003b), convective plumes and ramp-like structures (Thorpe, 1988;
Soloviev, 1990), and sharp frontal interfaces (Soloviev and Lukas, 1997b).
These structures are considered in detail in Chapter 5.
The transilient (Stull and Kraus, 1987) and large eddy simulation (LES,
Skyllingstad et al., 1999) models involve some nonlocal features. Diffusive
models, which are based on the parameterization of turbulent transports by
eddy coefficients, are essential local. Systematic incorporation of the
coherent structures into subgrid parameterizations is one of the important
tasks to be performed for improving mixed-layer models.
3.5.3 Rotation effects
On a rotating sphere with no stratification effects, the boundary layer
depends on the two components of rotation:
2 sin
f
M
:
and
2 cos
y
f
M
:
, where : is the magnitude of the Earth’s rotation vector and
Mis the latitude. The Coriolis parameter f contributes to the Ekman length
scale,
/
E
L u f
. An interesting situation is observed at the equator because
f vanishes; the classic Ekman layer is too deep there to influence strongly the
Chapter 3: NEAR-SURFACE TURBULENCE
215
with the idea by Stommel (1960) that the shear within the mixed layer is
proportional to the friction velocity. For the vertical eddy viscosity, Ekman
(1905, cf. Santiago-Mandujano and Firing, 1990) proposed a
parameterization
2
*
~
M
K
u , which is not consistent with the logarithmic
layer asymptote observed for neutral stratification conditions in the mixed
layer. The analysis of Santiago-Mandujano and Firing (1990) shows that
Ekman’s parameterization
2
*
~
M
K
u appears as a result of assuming that the
mixed layer depth is proportional to the Ekman scale,
* /
E
L u f . Ekman’s
parameterization ignores any dependence of M
K on depth z.
The boundary layer parameterizations (3.105) and (3.106) results in
~
M
K
u , which is consistent with the logarithmic layer asymptote
M
K
u z
N . The parameterization of Large et al. (1994) based on boundary
layer scaling also implies that
~
M
K
u .
An important feature of turbulence that has to be taken into account in
mixing parameterization schemes is that it is a fundamentally nonlocal
process (Stull and Kraus, 1987; Large et al., 1994). This is because the
turbulent transport is performed via a cascade of eddies. The nonlocal
behavior of turbulence is associated with the presence of spatially coherent
organized motions. There are numerous observations of coherent structures
in the surface layer of the ocean, including Kelvin-Helmholtz billows
(Thorpe, 1969), Langmuir cells (Weller and Price, 1988; Thorpe et al.,
2003b), convective plumes and ramp-like structures (Thorpe, 1988;
Soloviev, 1990), and sharp frontal interfaces (Soloviev and Lukas, 1997b).
These structures are considered in detail in Chapter 5.
The transilient (Stull and Kraus, 1987) and large eddy simulation (LES,
Skyllingstad et al., 1999) models involve some nonlocal features. Diffusive
models, which are based on the parameterization of turbulent transports by
eddy coefficients, are essential local. Systematic incorporation of the
coherent structures into subgrid parameterizations is one of the important
tasks to be performed for improving mixed-layer models.
3.5.3 Rotation effects
On a rotating sphere with no stratification effects, the boundary layer
depends on the two components of rotation:
2 sin
f
M
:
and
2 cos
y
f
M
:
, where : is the magnitude of the Earth’s rotation vector and
Mis the latitude. The Coriolis parameter f contributes to the Ekman length
scale,
/
E
L u f
. An interesting situation is observed at the equator because
f vanishes; the classic Ekman layer is too deep there to influence strongly the
Chapter 3: NEAR-SURFACE TURBULENCE
215