**1. Introduction**

128 Hydrodynamics – Natural Water Bodies

Zavatarelli, M. and Mellor, G.L. (1995). A numerical study of the Mediterranean Sea

circulation. *Journal of Physical Oceanogr*aphy, Vol. 25, pp. 1384-1414.

*Marine Systems*, Vol. 3, pp. 179-190.

Mediterranean in relation to the physical structure of the water mass. *Journal of* 

An interesting mesoscale feature of continental and shelf sea is the plumes produced by the continuous discharge of fresh water from a coastal buoyancy source (rivers, estuarine or channel).

The general spreading of freshwater plume depends on a large number of factors: tide, out flowing discharge, wind, local bathymetry, Coriolis acceleration, inlet width and depth.

The discharge of freshwater from coastal sources drives an important coastal dynamic, with significant gradients of salinity. These phenomena are highly dynamic and have several effects on the coastal zone, such as reducing salinity, changing continuously the vertical profiles and distribution of parameters, such as dissolved matters, pollutants and nutrients (Jouanneau & Latouche, 1982; Fichez et al., 1992; Grimes & Kingford, 1996; Duran et al., 2002; Froidefond et al., 1998; Broche et al., 1998; Mestres et al., 2003; Mestres et al., 2007).

As a result of these effects, several classification schemes based on simple plume properties have been proposed in an attempt to predict the overall shape and scale of plumes. Kourafalou et al. (1996) classified plumes as supercritical and subcritical, according to the ratio between the outflow and the shear velocity. Yankovsky and Chapman (1997) derived two length scales based on outflow properties (velocity, depth and density anomaly) and used them to discriminate between bottom-advected, intermediate and surface-advected plumes, depending on the vertical and horizontal density gradients near the plume front; in spite of the absence of external forcing mechanisms in their theory, they correctly predicted the plume type for several numerical and real cases. Garvine (1987) classified plumes as supercritical or subcritical using the ratio of horizontal discharge velocity to internal wave phase speed and he later proposed (Garvine, 1995) a classification system based on bulk properties of the buoyant discharge.

Referenced plume studies present numerical modelling of the case, in situ observations (Sherwin et al., 1997; Warrick & Stevens, 2011; Ogston et al., 2000), satellite observations (Di Giacomo et al., 2004; Nezlin and Di Giacomo, 2005; Molleri et al., 2010) or aerial photographs (Figueiredo da Silva et al., 2002; Burrage et al., 2008). In several cases two techniques are coupled (O'Donnell, 1990; Stumpf et al., 1993; Froidefond et al., 1998; Siegel et al., 1999).

In this work a freshwater dispersion by a canal harbour into open sea is described in depth with the aim of a 3D numerical model and with the validation of in situ measurements carried out with innovative instruments. The measurements appear in literature for the first

Freshwater Dispersion Plume in the Sea: Dynamic Description and Case Study 131

conservation of mass and momentum for a typically well-mixed water column due to wind and tidal stirring. So the vertical momentum equation has been substituted by baroclinic pressure equation (8) where sea water density has been formulated according with the international thermodynamic equation of sea water based on the empirical state function of

> *S Su Sv Sw S S S DDk t x y z x x y y zz*

*T Tu Tv Tw T T T DDk t x y z x xy yzz*

*S* and T are salinity and temperature, respectively. *Dx ,DY* are horizontal eddy diffusivities

balance an E coefficient of vertical exchange is introduced for momentum which relates vertical Reynolds forces to the vertical gradient of horizontal components of velocities and

> *mRi E Le*

> > *<sup>g</sup>* <sup>2</sup> *Ri L e z*

 

<sup>1</sup> *<sup>z</sup> L z <sup>d</sup>* 

> *xz x <sup>u</sup> <sup>E</sup> z*

> *yz y <sup>v</sup> <sup>E</sup> z*

where m is a numeric parameter and *Ri* is the Richardson number in terms of vertical gradient of density (ρ) and of eddy kinetic energy (e) and L defined, according with Von

using adequate parameters substitutive of ρ and m. The adopted vertical scheme introduces eddy kinetic energy as a state function which requires its own dynamic equation for balance

*e eu ev ew e e e D D E SD*

*t x y z x xy yz z*

(numerical coefficient) and d distance of bottom (z=0) from surface (z=d).

() () ( ) (15)

*z* (, )

<sup>0</sup> *<sup>p</sup> ST g*

() () ( ) (7)

() () ( ) (9)

are vertical diffusion coefficients for mass and wheat. For vertical

0 *x y*

<sup>1</sup> 0 *x y*

(8)

exp (10)

(11)

(12)

(13)

(14)

0 *x yee*

) are defined similarly to E coefficients

UNESCO81 which links density to Salinity, Temperature and Pressure:

for *S* and T; k and k'

Kàrman, by

and conservation:

Vertical exchange coefficients for mass (k) and heat (k'

expressed by Kolmogorov e Prandtl as:

time. The investigated area relates to the coastal zone near Cesenatico (Adriatic Sea, Italy). The aim of this chapter is to describe the dynamic of freshwater dispersion and to show the results of the simulation of flushing, mixing and dispersion of discharged freshwater from the harbour channel mouth under different forcing conditions.

The chapter will be organized in the following sections:

