CIESM Congress 2004, Barcelona, article 0113

Rapp. Comm. int. Mer Médit., 37,2004

113

ON A POTENTIAL VORTICITY IDENTIFICATION OF THE NO-MOTION LEVEL USING ONLY

HYDROLOGIC DATA, WITH APPLICATIONS TO THE MEDITERRANEAN SEA

M. Kurgansky

1, 2

, and E. Salusti

Department of Atmospheric and Oceanic Physics, Faculty of Physics and Mathematics, University of Concepcion, Casilla 160-C,

Concepcion, Chile - kurgansk@udec.cl

A.M. Obukhov Institute of Atmospheric Physics, Academy of Sciences, Russia.

INFN, Phys. Dept., “La Sapienza” Rome University Piazzale A. Moro, 2

Rome, Italy, * ettore.salusti@roma1.infn.it

Abstract

The theory of potential vorticity for stratified ?uids in a rotating system is applied to potential temperature

and salinity S. These ‘tracer

potential vorticities’are used to obtain an absolute ?uid velocity that generalizes earlier formulations. Here we use not the steady absolute

velocity but only a vector

??×?

Sproportional to it. In this way, insight is gained into a purely hydrological identification of the no-motion

level. This is then applied to historical data of the Mediterranean Sea with interesting results.

Keywords: potential vorticity, no motion level

A classical problem

It is well known how from the measurements of marine temperature

and salinity one can obtain vertical gradients of the current velocity u

[1], [2]. Recently, oceanographers using the

-spiral theories have

greatly improved our theoretical understanding of these problems by

noting how in reality hydrologic data allow the identification of the

no-motion level [see 3 for a review]. A somewhat simpler relation for

steady currents was obtained in [4] that in addition utilizes only

potential temperature

and salinity Sdata set.

Here we restrict ourselves to a simpler results that gives not ubut

only a vector

??×?

Sproportional to it, to search for surfaces of no

absolute motion (NAM in the following) for steady or quasi-steady,

inviscid or viscous marine currents. This is then applied to historical

data of the Mediterranean Sea with good agreement between our

theory and other information.

The absolute velocity field

In a steady adiabatic case, assuming

, ,

calling

the water density, the most general representa-

tion is

(

, S)

??×?

(1)

where

(

, S) is an arbitrary function. We now consider potential

vorticities

and with as

the absolute vorticity. Application of the general Ertel’s vorticity

theorem and also the method [4] gives two formulas

(2)

(3)

where kis the unit vertical vector, gthe gravity and wthe vertical

velocity. According to (1-3) we focus our attention on the vector

??×?

S. In [4] it is shown that

??×?

Sis proportional to uif the

streamlines do not change their shape with time, even if |u| can be

(slightly) time-dependent. This single vector can moreover give

sufficient information about the NAM surfaces

The condition

??×?

S=0 is satisfied when or more

generally

, where

and

are arbitrary functions. When

is essentially inclined to the horizon, as it is typical in the southern

Mediterranean Sea, then we may take

or better

, as a first guess in order to arrive at

??×?

S=0 from

the above conditions.

No-motion surfaces in the Mediterranean Sea

The Mediterranean Sea has been studied for a particularly long

time, since the Phoenician and Greek civilizations. However only in

1961 G. Wüst [5] was able to present a realistic scheme of its general

circulation. The data set of

and Swe analyze is taken from the Atlas

Hydrologique de la Mediterranée [6], prepared by P. Guibout.

We start with transect 69-70 between the Libyan coast and Sicily

(Cape Passero), along 15°40

E for the winter season. Under the

MAW, the LIW core is rather superficial, at 350-400 m depth. There

is a sharp zone of strong shears of the current velocity in the upper 200

m, spreading from the Libyan coast till ~35°N. So a reasonable

surface can be identified with the S=38.60 surface, that is ~250 m

deep in the main part of transect between 32°30

-35°00

N, and then

rapidly shoals near the Malta Island.

Transect 65-66 from Cape Dimas, Tunisia, to Malta Island is rather

similar to the previous transect: a reasonable

surface is at 400-

300m depths, corresponding to an S = 38.30 - 38.60 layer while the

LIW core is at ~1000 m depth.

The transect 15-16 from Algeria to Toulon, along 6°E, is also

interesting. The core of LIW, with S = 38.50, is at ~400 m depth. At

south one can easily recognize the superficial core of MAW. A

reasonable

surface is evident only between Algeria, where it is

~170m deep, and the region at 39°30

-40°00

N, along the surfaces

S= 37.70 - 37.90. Near the French coast there is a very strong coastal

jet, ?owing westward, which doesn’t seem to have any no-motion

level.

All this look in agreement with the scheme of an eastward

superficial MAW surface current at south, ?owing opposite to the

underlying LIW, and of rather parallel ?ows of LIW and MAW at the

north. However, these are actually debatable points as discussed by C.

Millot and other authors in various articles (see [7], for a review).

It is obvious that there are still some serious difficulties regarding

the direct implementation of our theoretical results in the study of real

data, both from the observational and the computational standpoints.

So far, only the Mediterranean Sea, seen as a natural laboratory with

its sharp contrasts between different water masses and relatively dense

observational network, including historical data sets, can be used to

test our ideas, albeit in a preliminary way.

References

1-Fomin, I.M., 1964. The Dynamic Method in Oceanography. Elsevier

Oceanography Series. Elsevier Publ. Comp., Amsterdam-London-NY,

212p.

2-Wunsch, C., 1978. The North Atlantic general circulation west of 50

West determined by inverse methods. Rev. Geophys. Space Phys, 16: 583-

620.

3-McDougall, T., 1995. The in?uence of ocean mixing on the absolute

velocity vector. J. Phys. Oceanogr., 25: 705-725.

4-Kurgansky, M.V., Budillon G. and Salusti E., 2002. Tracers and

potential vorticities in ocean dynamics. J. Phys. Oceanogr., 32: 3562-

3577.

5-Guibout, P., 1987. Atlas Hydrologique de la Mediterranée. SHOM ed.,

Ifremer, Paris, 150 p.

6-Wüst, G., 1961. On the vertical circulation of the Mediterranean Sea.

J. Geophys. Res., 66(10): 3261-3271.

7-Fuda J.L., Millot C., Taupier-Letage I., Send U. and Bocognano J.M.,

2000. XBT monitoring of a meridian section across the western

Mediterranean Sea. Deep Sea Res. I, 47: 2191-2218.

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