Some Aspects of Turbulence Role in Oceanic Currents - Selected Topics of Computational and Experimental Fluid Mechanics - page 176

Fig. 1 The Ocean General Circulation as first depicted by Gordon ( 1986 )( a ) and Broecker ( 1987b )
( b ). Both figures show where the deep and cold water sink and the regions where those upwell

they are cooled by the cold winter air that streams off Canada and Greenland. These
waters, which arrive at 12-13 ⓦ C, are cooled to 2-4 ⓦ C. The Atlantic is a particularly
salty ocean, so this cooling increases the density of the surface waters to the point
where they can sink all the way to the bottom. The majority of this water flows
southward, and much of it rounds Africa, joining the Southern Ocean's circumpolar
current” (Broecker 1991 ).
Based on those early studies, the big picture of the circulation was driven by
the cooling at high latitudes. Recent studies have shown that the Southern Ocean
is more relevant for the closure of the Meridional Circulation (Marshall and Speer
2012 ). Nevertheless, the small scale mixing is an important quantity that needs to be
properly parametrized to be included in the General Circulation Models, as it has a
huge impact on the Climate (Broecker 1987a ; Rahmstorf 2003 ).

1.2 Turbulence in the Ocean

In general, turbulence is a concept which is rather hard to define. In this manuscript
turbulence intensity is defined as the rate at which energy is being transferred from
large scale features to smaller scales. From the classical fluid dynamics point of
view, most of the processes in the ocean are turbulent (large Reynolds numbers).
The turbulent parameters that are covered in this text are an effective diffusivity
which includes the parametrization of turbulence and is used on the GCM's. There
are several assumptions which will not be covered but one of the most important
is that the diapycnal mixing is the same for density, temperature and salinity, i.e.,
K ˁ = K S . The turbulent intensity is high enough to neglect the differential

diffusivity (Ruiz-Angulo 2007 ). The turbulent diffusivity, K , in the interior of the
ocean is of the order of

K T =

10 − 5 m 2

∼ / s. This quantity is inferred from the dissipation

rate of turbulent kinetic energy, ʵ , following the Osborn relationship (Osborn 1980 ):

N 2 , where

is the mixing efficiency and N 2 is the Brunt-Väisälä frequency, K = ʓ ʓ

defined as: