Jökull - 01.12.1966, Page 25

condition depends on the velocity profile as
well as on the efficiency of the vertical heat
transport, and hence on the regime of flow and
on the vertical eddy diffusivity in the boundary
layer. Molecular conduction of heat is of neglig-
ible importance since oceanic currents are
generally turbulent.
At this juncture, there are no criteria avail-
able for the determination of the regime of
flow in the bottom boundary layer. Priestley’s
criterion, discussed above, which indicates the
transition between the regimes of fully forced
and dominantly free convection in the boundary
layer of the atmosphere, refers to conditions at
a specific level. It can therefore not be applied
quantitatively to the boundary layer in the
oceans. We can only draw the cjualitative con-
clusion that a similar transition may occur at
a certain level in the bottom boundarv layer
when the negative Richarclson number at this
level exceeds an unknown critical value.
The situation in the oceans is complicated
bv the limited vertical extension of the deep
water Iayer which is affected by the terrestrial
heat flow. Moreover, tides and internal motions
cause a considerable oscillatory unrest. This
situation is aggravated by the fact that the
velocitv of these oscillatorv motions mav locally
be orders of magnitude larger than the average
velocity of the global deep currents. For ex-
ample, recent studies by Isaacs et al. (1966) of
the local flow conditions above the bottom in
the deep Pacific west of the northern Baja
California Coast indicate both local net velo-
cities and semidiurnal fluctuation of the order
of 2 X 10 —2 m/sec. This is more than one
order of magnitude larger than the average
northward velocity of the deep Pacific current.
The tendency of the boundary layer to build
up superadiabatic temperature lapse rates is no
doubt dependent on the anisotropy of the tur-
bulence. This follows from the fact that the
stability against free convection is enhanced by
both the vertical as well as the horizontal eddy
diffusivities, whereas the magnitude of the
lapse rate is inversely proportional to the verti-
cal eddy diffusivity. A high ratio of the hori-
zontal to the vertical diffusivitv is therefore
favorable.
We will now investigate the magnitude of the
vertical eddy diffusivity implied by the super-
adiabatic lapse rates reportecl by Lubimova et
al. (1965) as well as by Bodvarsson et al. (1967)
and compare the results with other estimates.
On the basis of an average terrestrial heat
flow of 0.06 watts/m2, the lapse rates of 10
to 10-2 °C/m correspond to a vertical eddy
cliffusivity az = q/scy = 1.5xl0“6 to 1.5xl0-4
m2/sec. These values fall within the lower part
of the range given by Sverdrup (1957).
An order-of-magnitude estimate of the aver-
age vertical eddv diffusivity in the upper séc-
tion of the Pacific deep current can probably
be obtained on the basis of the global changes
of the temperature and the salinity below 4,000
m on the passage to the North. The lower
section of the current can be approximated as
a very thin horizontal laver of a thickness h
and moving with a constant uniform velocitv u
in the direction of the x axis. For the present
purpose we can assume that this layer is heated
entirely by the vertical heat transport from
above. If yz is the gradient of the potential
temperature at the top of the layer, and yt is
the temperature gradient along the x axis, the
following relation,
az yz = uhVx> (!2)
can be applied in order to estimate az. The
same relation will hold for the salinitv changes
provided the gradients are interpreted as salinity
gradients. It is to be emphasized that the simple
model on which equation (12) is based disre-
gards the effect of the slow upwelling of deep
water which is known to take place in the
North Pacific. This difficulty can probably be
largely avoided by restricting the model to the
conditions in the South Pacific. However, the
order of magnitude of the above estimate is
apparently not affected.
The data diven by Knauss (1962) indicate
that the average potential gradient between the
depths of 3,500 and 4,500 m is of the order of
= 3 x 10-4 °C/m, and as already stated t.he
average horizontal gradient is yx = 5 x 10-8
°C/m. The thickness of the layer heated from
above is of the order of h = 103 m and the
average northward velocity is u = 10 -3 m/sec.
These values give on the basis of equation (12)
a vertical eddy diffusivity of az = 1.7 X 10-4
m2/sec.
According to Knauss (1962), the salinity of
the Pacific deep current is changed by a total
of —0.025 kg/m3 over a distance of 12,000 km.
JÖKULL 179