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

4.5. MEAN CIRCULATION AND STRUCTURES OF TILTED OCEAN DEEP CONVECTION105
804 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
regions, or second, by parameterizing the nonhydrostatic
effects.
The present work is an attempt toward the second
approach for the case of open-ocean convection. If such
parameterization is used, its implementation is most
likely to consume less computer power than a nested
nonhydrostatic model. Detailed research on the influence
of external parameters, such as, for example, magnitude
and direction of rotation, is integral to developing
and improving such parameterization and adjusting
the parameter values in existing parameterization.
Existing parameterizations of open-ocean convection
can be put into two categories. The first consists of
schemes that are driven by the necessity to remove the
convective instability with no reference to the physics
of convection. The second type includes some of the
physics of convection borrowed from atmospheric observations,
models, and convection schemes. They thus
exclude qualitative differences resulting from the different
Rossby numbers involved in the ocean and atmosphere.
Convection in the atmosphere takes only a
few hours, while it takes a few days in the ocean. We
will demonstrate that the corresponding difference in
Rossby number is essential for the convection process
and its parameterization. Oceanic convection is in a
dynamically interesting regime because vertical velocities
are large enough so that nonhydrostatic terms cannot
be ignored, but are small enough so that rotation
cannot be ignored either. Nonlinearity is strong enough
so that the dynamics are in a three-dimensional turbulent
regime, as opposed to quasi-two-dimensional heton
dynamics [see Klinger and Marshall (1995) for a
detailed discussion of the three-dimensional versus heton
regimes]. Furthermore, the results published in
Klinger and Marshall (1995) and those of the present
work indicate that away from the surface boundary
layer the convection process creates a vertical density
structure that has the characteristic that the influence of
(unstable) stratification is comparable to that of rotation.
We furthermore show that not only is the magnitude
of the rotation vector (as expressed in the Rossby number)
of importance, but so too is its direction. More
precisely, in the majority of numerical calculations considering
ocean dynamics, the traditional approximation
(see, e.g., Marshall et al. 1997) is employed, which completely
neglects the horizontal component of the rotation
vector, and thus its “tilt.” One exception is the
large-eddy simulation (LES) by Wang (2006). Rotation
is thus supposed to be collinear with gravity, which is
strictly only the case at the poles. The traditional approximation
may be justified in instances where vertical
velocities are small compared to their horizontal counterparts,
that is, when nonhydrostatic terms can be neglected.
However, when nonhydrostatic terms are essential
for the dynamics, as in the case of convection,
the horizontal component of the rotation vector (the
tilt) has to be included.
The important part of the tilt in the rotation vector
for the dynamics of a single convective plume in an
oceanic context was demonstrated experimentally by
Sheremet (2004) and numerically by Wirth and Barnier
(2006). The dynamics of a collection of plumes generated
by homogeneous forcing (cooling) at the surface
cannot be deduced from the dynamics of a single plume
due to the nonlinear interaction between the plumes
with the turbulent background and the density stratification.
It is thus of paramount importance to investigate
the possible changes of ocean convection when
subject to a homogeneous forcing at the surface.
The important consequences of two buoyant tracers
(temperature and salinity) and a nonlinear equation of
state are the subject of future research and are not
considered here.
To summarize: open-ocean convection is a dynamically
very involved process, where rotation (magnitude
and direction), vertical acceleration, stratification, and
three-dimensional turbulence (nonlinearity) each play
a role of almost equal importance. That is, none of the
terms in the Boussinesq equations can be neglected and
none are dominant.
In the next section we discuss some basic facts of
open-ocean convection with an emphasis on its integral
effects, which are important when a parameterization is
to be constructed. We then proceed by explaining the
physics of our experiment, followed by a description of
the mathematical model and its numerical implementation
used for our investigations of deep convection in
section 3. Results of our numerical experiments are
presented in section 4. In section 4a, the imprint of the
Taylor–Proudman–Poincaré (TPP) theorem on the
structures of the turbulent convection process is shown,
and in section 4b the horizontal mean temperature
structure is discussed and the generation of mean horizontal
velocities is demonstrated analytically and experimentally.
The values of second-order moments essential
to many parameterization schemes are determined
and discussed in section 4c. We conclude in
section 5 by discussing the implications of the herepresented
results on the large-scale ocean dynamics.
2. Open-ocean deep convection
a. Basic facts
The entire deep-ocean convection process is usually
divided into the following three phases: (i) precondi-