Etudes et évaluation de processus océaniques par des hiérarchies ...

4.7. ON THE BASIC STRUCTURE OF OCEANIC GRAVITY CURRENTS 137
Ocean Dynamics (2009) 59:551–563 557
Fig. 3 Structure and vertical velocity field at 24 h in exp. G15.
The temperature anomaly, with respect to the ambient water,
is shown (given in Kelvin). Isolines of the w component of the
velocity are given in black for positive values (upward) and
red for negative values; the contour lines shown are ±10 −5 , 3 ·
10 −5 , 10 −4 , 3 · 10 −4 , 10 −3 , 3 · 10 −3 ; the logarithmic scale was chosen
due to the large intermittency of the vertical velocity. Vertical
velocities outside the vein are due to wave-like motion of the
interface
tel-00545911, version 1 - 13 Dec 2010
shows only a small variation during the evolution of
the gravity current. This shows that there is no substantial
entrainment or detrainment for the total gravity
current.
The density anomaly and the along-slope velocity (y
component) both decrease in the experiments. To leading
order, the dynamics is supposed to be given by the
geostrophic equilibrium as discussed in Subsection 2.1.
To verify this, I calculate the along-slope velocity component
in the vein divided by the geostrophic speed of
its reduced gravity, given by: v G = (g ′ /f) tan α, for each
density class within the vein. When the average for all
parcels in the vein which are at least 20 m above ground
is analysed, the average along-slope velocity decreases
to about 95% the geostrophic velocity after 2 days.
This shows that the gravity current progresses along
the slope at almost geostrophic speed, in agreement
with previous findings of Price and Baringer (1994) and
others.
Friction leads to a downslope transport of gravity
current water. The dynamics of the vein differs completely
from the dynamics of the total gravity current,
and so does their rate of descent and their spreading,
as can be verified in Fig. 4. The spread and descent of
the gravity current, which includes the friction layer, is
much larger than that of the vein alone.
Figure 4 shows that the depth of the upper bound
of the vein stays almost constant, a feature that is
well documented (see Price and Baringer 1994 and
references therein), while the downslope sides of the
vein and the friction layer descend. At the upslope
side, the y component of the velocity vector is negative,
as noted above, the fluid in the Ekman layer should,
thus, move upslope. This leads to an arrested Ekman
layer, as explained by Garrett et al. (1993), and no
friction layer forms at the upslope side of the gravity
current. The speed of descent of the downslope front
of the friction layer slightly decreases with time due
to the decrease of its density anomaly. Indeed, there
is a no-slip boundary condition at the ocean floor, the
water right above it cannot keep up with the downward
speed of the front of the gravity current and gravity
current water superposes surrounding water near the
downward progressing front. This surrounding water
becomes mixed into the friction layer near the front
and dilutes the gravity current water near the downward
progressing front, a feature common to all gravity
currents.
The descent of the centre of gravity of the vein is
well fitted by a linear law (see Fig. 4). The rates of
descent are given in Table 2. The angle of descent of
the vein compares well to the theoretically predicted
value of 1.2 · 10 −2 , based on a linear force balance
Fig. 4 The lower and upper bounds along the slope of the gravity
current (black curves) and the vein (red curves) are shown. That
is, the gravity current evolves (in time) between the black lines
and the vein between the red lines. The vein is defined to be the
part of the gravity current more than 20 m above ground. The
path of the centre of gravity of the total gravity current (green
line) and the vein only (blue line) are also shown. All the results
are from exp. G03; other experiments show the same qualitative
behaviour