Geoscience Reference
In-Depth Information
c
g
= U
-
2
7
x 10
-
3
6
5
a
4
3
2
0
0.1
0.2
0.3
0.4
0.5
Angle between V
s
and
τ
0
30
b
25
20
15
0
0.1
0.2
0.3
0.4
0.5
V
s
(m s
-
1
)
Fig. 4.6
DragcoefficientfromRossbysimilarity.
a
magnitude.
b
Turninganglebetweenstressand
surface velocity
underside,and possibly modifythe amountof Ekmandeflection in ice drift.In this
section,we consideranextensiontothesimilarityapproachthatincludesbuoyancy
flux (McPhee 1981,1983).We seek a similarity solution to the Ekmanstress equa-
tionthatincludestheeffectsofsurfacebuoyancyflux.
WepostulatedearlierthatthereisamaximummixinglengthintheneutralIOBL
given by
Λ
∗
is a “universal” similarity parameter. As sta-
bilizingbuoyancyaffects turbulence,we anticipate that turbulencescales including
λ
λ
max
=
Λ
∗
u
∗
0
/
f
where
max
will decrease. Its lower limit follows from considering the simplified TKE
equationwiththesurfacelayerapproximationofconstantflux
z
−
w
b
0
=
u
∗
0
3
λ
−
w
b
0
=
ε
P
b
=
τ
·
∂
u
P
s
+
(4.21)
∂
Dividingthroughby
P
s
P
b
P
s
=
−
λ
κ
R
f
=
ελ
u
∗
0
3
1
+
1
L
=
1
−
(4.22)
The key here is that the ratio of buoyancy flux to shear production, called the
flux
Richardson number
hasalimitingcriticalvalue,
R
c
,beyondwhichturbulenceceases
to exist in laboratory flows. A commonly accepted value is around 0.2. Thus for
turbulenceto beviable
