Jökull - 01.12.1966, Page 26

The average horizontal salinity gradient is thus
of the order of yx = — 2 X 10-9 kg/m4. The
average vertical salinity gradient between the
depths of 3,000 and 4,000 m is of the order of
Yz = — 3xl0~5 kg/m4. The thickness of the
layer affected by the dilution from above can
be estimated at h = 1.5 X 103 m. Using the same
average velocity as above equation (12) gives
for the vertical eddy diffusivity a value of
az = 10-4 m2/sec. It is to be realized that this
figure, as well as the above figure obtained on
the basis of the temperature gradients, applv
to the section between the depths of 3,000 and
4,500 m.
It is tempting to use the horizontal tempera-
ture gradient at the bottom of the Pacific deep
current in order to estimate the vertical eddy
diffusivity there on the basis of equations (9)
and (10). Here we have to face the problem of
the finite thickness of the current and the ver-
tical transport of heat from above. However,
equation (10) can possibly be applied to the
temperature rise near to the origin of the
current, since it can be expected that the finite
thickness is of less importance there. According
to Knauss (1962) the temperature at the depth
of 5,000 m increases from the latitude 55° S
to that of 40° S by approximately 0.1° C. Using
this value in combination with x= 1.8 X 106
m, q = 0.06 watts/m2 and u = 10-3 m/sec. we
find on the basis of equation (10) a vertical
eddy diffusivity of az = 4.5 X 10-5 m2/sec.
Since the depth of the ocean in this region is
only slightly in excess of 5,000 m this value
should apply to the lowest section of the cur-
rent. This estimate is necessarily quite un-
certain. The result is subject to the condition
that the thickness of the bottom layer affected
mainly by the terrestrial heat flow exceeds a
certain minimum, which in the present case
will be of the order of 1 km. Moreover, the
situation in the southernmost part of the Pacific
deep current appears to be rather complex.
Finally, Knauss (1962) points out that the
deep waters in the vicinity of the East Pacific
Rise have abnormally high temperatures, which
may result from a local terrestrial heat flow
anomaly. Data from the depth of 3,000 m
indicate a local temperature rise of the order
of 0.1 to 0.2° C. The main heat flow anomaly
is on an approximately 1,000 km wide strip
along the 110° W meridian. The average excess
180 JÖKULL
heat flow within the strip appears to be of the
order of 0.1 watts/m2. The axis of the maxim-
um temperature anomaly in the water appears
to be shifted by approximately 2,000 km to
the SE of the center axis of the strip.
For the purpose of an order of magnitude
estimate of the vertical eddy diffusivity in the
area, we can approximate the strip by a con-
tinuous line source of heat and use the magni-
tude of the horizontal shift of the maximum
temperature anomaly from the center axis of
the heat flow anomaly in order to estimate the
coefficient b = az/u. The solution of the dif-
fusion equation (3) for the case of a continuous
infinitely long line source of the specific
strength Q which is placed along the y axis in
the lower boundary of a semi-infinite medium,
is given by Sutton (1953)
Q
0 = --=5T=exp(-z2/4bx), (13)
V 2-n-a^x
where the same nomenclature has been used as
in paragraph (3). The function given in (13)
has a maximum for z2 = 2bx. The maximum
of the temperature anomaly at a level z is thcre-
fore shifted by a horizontal distance of x =
z2/2b from the line source. Using the average
values of z = 500 m and x = 2,000 km we find
a coefficient of b = 0.06 m. Assuming velocities
varying from u = 10~3 to 10~2 m/sec. we find
the eddy diffusivities of az = 6xl0“5 to
6 x 10~4 m2/sec. The estimates suffer from
lack of information on currents in the area.
However, since the velocity u in equation (13)
represents the average velocity unaffected bv
oscillatory motions it appears likely that u is
of the same order as the northward velocity
of the main deep current. Hence the lower
estimate of roughly az = 10~4 m2/sec. appears
more likely. This should represent an average
for the lowest 500 to 1000 meters.
Summing up the above results, we find for
the Pacific deep current eddy diffusivities rang-
ing from 4.5 X 10~5 to 1.7 X 10-4 m2/sec. The
lowest value is found in the lowest section of
the current between 55° S and 40° S. These
values are about. the average of the values given
by Sverdrup (1957), but they are one or two
orders of magnitude lower than the values com-
puted for the deep Atlantic currents by Wust
(1955). The difference may result from the