THE NEAR-SURFACE LAYER OF THE OCEAN
1.2.3 Low Rossby number approximation
Further simplification of equations (1.6)-(1.7) is possible under the low
Rossby number,
l
,
(1.16)
where u l is the typical velocity scale, l is the length scale characteristic of
horizontal variation of properties in the ocean, and f is the Coriolis
parameter. Under the boundary layer and low Rossby number
equations to:
1
1 zx
u
p
fv
t
x
z
W
U
U
w
w
w
w
w
w
,
(1.17)
1
1 zy
v
p
fu
t
y
z
W
U
U
w
w
w
w
w
w
.
(1.18)
unaffected by the low Rossby number approximation since the Coriolis term
does not enter into those scalar equations.
1.2.4 Turbulence and turbulent kinetic energy budget
In the ocean, the diffusion processes are usually associated with
turbulence. Turbulence can occur because of local (shear or convective) flow
instability or may be transported from a nonlocal source by advection,
convection, or turbulent velocity and pressure fluctuations. An important
source of turbulence in the upper ocean is surface wave breaking (Chapter
3).
The criterion for shear instability commonly used in hydrodynamics is
the Reynolds number,
Re
/
l
u l Q
(1.19)
where u l is the velocity scale, Q is the molecular coefficient of kinematic
viscosity (
6
10
1
.
1
˜
Q
m
2 s
-1 at T = 20
o C and S = 35 psu), and l is the
8
1
Ro u / lf
approximations, the advective terms in equations (1.6)-(1.7) vanish reducing
these
Equations (1.10)-(1.12) for the heat, salinity, and other substances are