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

132 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES
552 Ocean Dynamics (2009) 59:551–563
tel-00545911, version 1 - 13 Dec 2010
momentum are neglected, rotating gravity currents flow
along the inclined ocean floor changing neither depth
nor composition. Turbulent fluxes of tracers, that is
mixing, entrainment and/or detrainment, determine the
change of the water mass. Together with the turbulent
fluxes of momentum at the floor and interface of the
gravity current, they govern the pathway and the composition
of the gravity current. Oceanic gravity currents
are thus subject to three forces: (1) the buoyancy force
pointing downslope, (2) the Coriolis force directed at a
right angle to the direction of motion and (3) frictional
forces due to dissipative fluxes of mass and momentum
(see Fig. 7 in the Appendix). The first two forces are
linear, the total buoyancy force depends linearly on the
total buoyancy anomaly and the total Coriolis force is
a linear function of the transport of the gravity current.
The above shows that the answer and problem of the
evolution of a gravity current lies in the determination
of the laws and parameters of its dissipative fluxes
of momentum and mass. For an introduction to the
dynamics of oceanic gravity currents, I refer the reader
to Griffiths (1986).
In the past 30 years, the study of streamtube models
has greatly increased our understanding of the dynamics
of oceanic gravity currents. In streamtube models,
only average (bulk) values of the dynamical variables
are considered at every cross section along the path
of the gravity current (see Smith 1975, 1977; Killworth
1977, 2001; Price and Baringer 1994; Baringer and Price
1997; Emms 1998). Due to their linear nature, the
integrated buoyancy and Coriolis force can be calculated.
The nonlinear frictional forces and the turbulent
fluxes, perturbing the geostrophic equilibrium, have to
be parametrised. The evolution of the gravity current
can then be studied as a function of the parametrisations
and parameter values employed. Integrations
of these semi-analytical streamtube models along a
path of varying topographic slope are performed and
the parameter values are adjusted in such a way that
the pathway and water mass characteristics compare
favourably to observations. This adjustment procedure,
however, does not always lead to a deeper understanding
of the physical processes involved (see Emms
1998). The implementation of streamtube models or
their physics in large-scale ocean general circulation
models is difficult. Although progress has been made in
better representing gravity currents in large-scale ocean
general circulation models through bottom boundary
layers (see, e.g. Killworth and Edwards 1999; Price and
Young 1998; Wu et al. 2007), their dynamics is still
a weak point of today’s numerical models of ocean
circulation.
Many efforts have been undertaken to determine
the turbulent fluxes from observations, laboratory experiments
and numerical simulations, but no definite
conclusion has been reached, no generally accepted
parametrisation is available and no generally accepted
parameter values have been obtained so far. As an
example, a key parameter is the entrainment rate; there
is, however, no definite answer even about its sign
in rotating gravity currents (Ezer 2005; Legg et al.
2006). Killworth (2001) states that “entrainment should
only occur over limited regions, with detrainment elsewhere”,
and MacCready notes that “[...] the majority of
entrainment with overlying waters occurs close to the
overflow sill [...], and is largely negligible there after”.
Furthermore, Ermanyuk and Gavrilov (2007) found
in laboratory experiments on non-rotating gravity currents
that the dissipative processes at the interface have
a negligible role compared to those due to bottom
friction.
The purpose of the present work is to determine the
basic processes and structure of oceanic gravity currents
in an idealised configuration as a testing ground
for present and future models and parametrisations in
basin scale models. To this end, I will numerically integrate
the (nonhydrostatic) Navier–Stokes equations.
With respect to streamtube models, I will not try to adjust
parameter values so that they compare favourably
to observation, but I will instead test the hypotheses
they are based on by comparing their assumptions with
our results from the Navier–Stokes model of highly
idealised gravity currents. I show that gravity currents
actually consist of two parts and that this two-part
structure is key to understanding and modelling their
dynamics.
In his pioneering paper on the dynamics of viscousrotating-gravity
currents, Smith (1977) stated, concerning
their structure, “[...] a complete solution remains
inaccessible” (Section 3, lines 7–8). I will here demonstrate
that the structure, evolving in time, of idealised
gravity currents can be obtained by solving a onedimensional
heat equation. Results on the basic structure
of idealised oceanic gravity currents are also the
starting point for the large-scale, three-dimensional instability
analysis leading to the formation of coherent
cyclonic structures (Meacham and Stephens 2001). The
important dynamics of large-scale instability is not considered
in this work.
The model is introduced in the next section, results
are presented in Section 3 and they are discussed in
Section 4, where I also consider the consequences of
our results for the representation of oceanic gravity
currents in ocean general circulation models (OGCMs).