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

4.7. ON THE BASIC STRUCTURE OF OCEANIC GRAVITY CURRENTS 131
Ocean Dynamics (2009) 59:551–563
DOI 10.1007/s10236-009-0202-9
On the basic structure of oceanic gravity currents
Achim Wirth
Received: 2 February 2009 / Accepted: 27 April 2009 / Published online: 15 May 2009
© Springer-Verlag 2009
tel-00545911, version 1 - 13 Dec 2010
Abstract Results from numerical simulations of idealised,
2.5-dimensional Boussinesq, gravity currents on
an inclined plane in a rotating frame are used to determine
the qualitative and quantitative characteristics
of such currents. The current is initially geostrophically
adjusted. The Richardson number is varied between
different experiments. The results demonstrate that
the gravity current has a two-part structure consisting
of: (1) the vein, the thick part that is governed by
geostrophic dynamics with an Ekman layer at its bottom,
and (2) a thin friction layer at the downslope side
of the vein, the thin part of the gravity current. Water
from the vein detrains into the friction layer via the
bottom Ekman layer. A self consistent picture of the
dynamics of a gravity current is obtained and some of
the large-scale characteristics of a gravity current can
be analytically calculated, for small Reynolds number
flow, using linear Ekman layer theory. The evolution of
the gravity current is shown to be governed by bottom
friction. A minimal model for the vein dynamics, based
on the heat equation, is derived and compares very
well to the solutions of the 2.5-dimensional Boussinesq
simulations. The heat equation is linear for a linear
(Rayleigh) friction law and non-linear for a quadratic
drag law. I demonstrate that the thickness of a gravity
Responsible Editor: Eric Deleersnijder.
A. Wirth (B)
LEGI / MEOM, CNRS, BP 53, 38041
Grenoble Cedex 9, France
e-mail: achim.wirth@hmg.inpg.fr
current cannot be modelled by a local parameterisation
when bottom friction is relevant. The difference between
the vein and the gravity current is of paramount
importance as simplified (streamtube) models should
model the dynamics of the vein rather than the dynamics
of the total gravity current. In basin-wide numerical
models of the ocean dynamics the friction layer has to
be resolved to correctly represent gravity currents and,
thus, the ocean dynamics.
Keywords Ocean dynamics · Gravity current
1 Introduction
Buoyancy forces caused by density differences in fluids
are a major source of fluid motion in nature. When
these forces act adjacent to topography, gravity currents
are created. The major part of the deep and
intermediate waters of the world ocean and marginal
seas have done at least part of their voyage to the
deep in the form of a gravity current. Oceanic gravity
currents play a role of paramount importance in the
formation of the water masses and the ventilation of
the deep ocean and are thus key to understanding the
oceanic component in the earth’s climate system.
For most oceanic gravity currents, the earth’s rotation
plays an important role, as they evolve on
a timescale much larger than the rotation period
of the planet earth. The dominant force balance is
thus between gravity and the Coriolis force, that is,
geostrophic. Research on non-rotating gravity currents
cannot be extrapolated to the rotating case, as it ignores
this leading order balance. When the turbulent (and
the neglectable molecular) fluxes of water masses and