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

4.5. MEAN CIRCULATION AND STRUCTURES OF TILTED OCEAN DEEP CONVECTION113
812 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 38
tel-00545911, version 1 - 13 Dec 2010
FIG. 6. Horizontally and temporally averaged temperature gradient z T h, t (see Table 2 for
experiments).
on the surface buoyancy flux (B 0 ), which is consistent
with dimensional analysis, the second derivative of the
mean temperature with respect to the vertical is thus
constant, zz T h,t 2/3 H 7/3 /(g), where we estimated
the dimensionless constant 10.
In all of the results on temperature and its vertical
gradients no significant difference between the nontilted
and tilted case could be detected, except for the
differences in the bottom Ekman layer. Also of great
importance is the observation that in the lower 500 m
the temperature gradient is positive, which means that
there is a countergradient flux of heat. This behavior is
often named “nonlocal transport,” and it is caused by
the buoyancy transport of the convective plumes that
extent from the surface to the bottom of the domain.
Fitting an affine law to the gradient of the depthaveraged
temperature allows the buoyancy flux to be
written as
Z g z T B 0z
H ,
12
where denotes the nonlocal part of the flux. Equation
(12) is taken from the KPP parameterization (see Large
et al. 1994), and the term on the right-hand side is a
consequence of the stationarity of the dynamics. Dimensional
analysis suggests Z 0 (B 0 H 4 ) 1/3 , where
the dimensionless constant 0 1 0.1 best fits our
data, leading to Z 40 m 2 s 1 for experiments E01
and E31, and a heat flux of only 250 W m 2 leads to an
eddy diffusivity of about Z 5 m 2 s 1 for a convection
depth of 1 km. In OGCM calculations a constant eddy
diffusivity of Z 10 m 2 s 1 , independent of depth and
buoyancy forcing is often employed, which lies in between
the values obtained here.
If we deduce from Fig. 6 that the temperature gradient
is zero at about 500 m from the ground, we can
obtain a nonlocal (countergradient) heat flux of about
1/7th of the heat flux at the surface. Dimensional analysis
gives 0 (B 0 /H 2 ) 2/3 , with 0 1/7.
We would like to emphasize that the total vertical
heat flux is always positive (negative temperature perturbations
being transported downward), and decreases
linearly from the maximum value at the surface to zero
at the floor. In our calculations we cannot have an upward
heat flux, which is often observed when convection
into a stratified medium is considered, because in
our experiment the lower boundary is the completely
insulating ocean floor.
2) VELOCITY
Due to the top and bottom boundaries and the incompressibility
of a Boussinesq fluid, the horizontally