Chemistry Reference
In-Depth Information
two independent non-dimensional quantities can be formed from them, any
possible relation will be of the form
2
3
U
U
§
·
max
k
k
f
¨
©
¸
¹
U
k
Q
k
where
f
(
x
) is an unknown function. The relation (8) with
N
w
= const. corre-
sponds to the case
f
(
x
) = const, while the relation (4) corresponds to
f
(
x
) v
x
-1/2
.
3. Motion on different scales
The surface motion is of many scales, spanning from mm-waves to meso-
scale eddies. In our discussion perhaps the range 10
-1
to 10
3
meters is of in-
terest. Surface slicks are only observed for relatively low and moderate
winds. The surface motion during slick conditions may, however, be the
result of earlier wind induced turbulence and Langmuir cells in the upper
ocean layer. Small scale motion (of the order of 10 cm or less) is probably
due to a convective motion in a shallow surface layer (Gemmerich and
Hasse 1992).
Let us first consider the surface flow caused by turbulence in the bulk.
While moving towards the surface, the vertical velocity fluctuations are
disappearing and the horizontal ones seems to have the same wave number
scaling as in the bulk (Kumar et al. 1998, Eckhardt and Schumacher 2004).
If the turbulence in the bulk has an inertial range with a Kolmogorov type
spectral variation, then the induced surface divergence
kU
k
(at a clean sur-
face) scales like
k
-1/3
i.e. a rather weak dependence on
k
, and the right hand
side of equation (7) scales like
k
1/4
. On the other hand the quantity
(
U
k
3
/
k
)
1/2
appearing in equation (4) would be expected to scale like
k
-5/2
. So
over the inertial range the longest scales would be likely to dominate the
tearing, while the compacting have an insignificant variation with scale in
the same range.
For scales comparable or exceeding the depth of the mixed layer it
seems reasonable to assume that the arrangement of surface film material
is dominated by stronger and more coherent motions like Langmuir cells
and fronts with downwelling. The structures seen in SAR images have a
number of different scales. The basic ones being the filamentary structures
with transverse dimensions of the order of 100 m and longitudinal coher-
ence of several kilometers. Even the smaller eddies (order of 10 km) are
visualized by the bending of this smaller scale striation. There is, however,
an upper limit to the ocean scale induced arrangement of slicks, because a
