Transport Processes of Suspended Matter in the Gulf of Gaeta

Transport processes of suspended matter in the

Gulf of Gaeta

L. ~rieco'& G. ~udillon' I Meteorology and Oceanography Institute, University of Naples

"Parthenope", Italy.

Abstract

In this work a dispersion model is used in a process study to simulate the suspended matter fate in the Gulf of Gaeta. In the last years the protection of its coasts is one of the most peculiar problems.

In the time the human impact has changed the natural processes: the flux of suspended matter from rivers has been decreased through the building of dikes and containment barriers, and the growth of industrial and tourist activity along these areas has been led the destruction of dunes representing a natural reserve of

sand. In view of dredge offshore operations to restore the beaches in erosion, the suspension matter subject to the circulation present, could generate new damages to the coastal area. Moreover some Posidonia meadows have been identified in

the neighbouring of the dredge area and the released sediment may damage them. Therefore it is clear the importance of a study that is able to estimate the transport processes in the examined area.

1 Introduction

The primary objective of this work is the investigation of the small-scale physical processes about the dispersion and sinlung processes. The examined area is the Gulf of Gaeta located between Rome and Naples 1). (figure

1 26 Water Pollution \//I: Modclling, Mca~uringand Prediction

Figure 1: Gulf of Gaeta.

Gaeta is one of the most important tourist seaside resorts of the Tyrrhenian coast with its sandy beaches and sweet slope of the bottom, but unfortunately it is subject to a drastic molphological evolution. The meteorological and marine conditions and, above all, the anthropical influence cause the continuum erosion of same beaches and the silting up of the others. Recent studies pointed out the presence of sandy reserves in the offshore area to be used in the restore of the beaches, such as in front of Scauri, sideways on P.ta del10 Stendardo.

The dredge operations, however, involve suspension matter subject to the circulation present and close to the dredge area some relevant Posidonia meadows are known. Therefore a numerical multi-level model has been developed fox a diagnostic study about dispersive processes of variable grain size sediment.

2 Description of the model

The dispersion processes have been studied according a Eulerian approach that analyses the spatial and temporal variability of a tracer. The tracer dispersion processes is assumed to obey the following advection- diffusion-sedimentationequation

The variable C(x, to) represents the concentration of the examined substance and

KH (Kv) is the horizontal (vertical) eddy-diffusivity parameter, while Vsed represents the sedimentation velocity

where g is the gravity (m/s2), p is the water viscosity (kgls), d the mean diameter of the parcel (m), pp the density of the released tracer and p" the density of the water at the level of the realise (kg/m3). The initial condition is a Gaussian distribution

with COis the maximum concentration released, the standard deviation o = 0.5 and (%,yo,zo)the release point.

The boundary conditions at the fluid boundary simulate an inflow (u.n <0) and outflow (u.n >O) condition while at the bottom no flux condition is imposed.

2.1 Description of the eulerian model

The scheme used in the model is based on the numerical method of lines, a versatile approach to the solution of time-dependent PDEs, which basically proceeds in two steps [l]: a) approximation of spatial derivatives using finite difference, finite element or finite volume methods b) time integration of the resulting system of semi-discrete initial value equations using ODE solvers

Then in the horizontal plane the spatial discretization is separated from the temporal discretization according to the scheme

where Ci(t) is a continuos function of the time and it is an approximation of the concentration C(xi,t) in the point xi=idx, i=1,2. . . ; FitlIZ represents an approximation of the flux, defined as the mass that in the temporal range crosses the unit area: F=-V. (UC) at centre of the i-th cell; KH and K" are the horizontal diffusive coefficient and the vertical eddy diffusivity, which order of, respectively, of 105cm2S-' and 10-'cm2S-' [S], [6] and [7].

For the spatial discretization of the advective term, attention is confined to conservative schemes using an upstream method of the third order (using 5 points for direction) [2]. This scheme is used in the region without steep concentration gradients, while a scheme of order lower, but a positive scheme llke the upwind method of the first order, is used in the region in whch the negative concentration can be exit. The automatic selection between the two

1 28 Water Pollution \//I: Modclling, Mcaburing and Prediction

schemes is done through the introduction of a non linear function of the flux, (flux limiting), that acts by a switch between the methods. Then the positively is enforced through flux limiting (for more details see Hundsdorfer et al. [2] and

Riccio [3]).The sedimentation term has been discretized trough an upstream method of the first order, while the spatial discretization of the diffusive term (both horizontal and vertical) has been solved classically through a central difference scheme. The temporal advancement is leaded according to an explicit scheme using a Runge-Kutta method of the second order

3 Data analyses of the velocity field

Before discussing the transport properties, we briefly report the surface circulation as revealed by measurements carried out by the Meteorology and Oceanography Institute (University "Parthenope" of Naples) and performed in

the area between Del10 Stendardo Cape and Garigliano River on February 2002.

Figure 2: Gulf of Gaeta and velocity field measured.

The measurements reveal a longitudinal south-eastward transport with mean surface current of order 20-30 cmls which probably is the cause of the erosion of

two areas: Vindicio e S.Janni beaches (Forrnia) and Scauri (Minturno) (fig.1). Moreover in this littoral zone a sandy deposit stands out at 11Km offshore along the bathymetric between -50mt and -70mt (red square), that could be utilised for the restore of this area (http:l/www.llpp.regione.lazio.i~opere/MARE/tema).

In order to simulate the release of sediment in the deposit region, where dredge operations could be done, the velocity field measured in some location (fig.2) has been interpolated on a grid of 26x27 points, with a spatial resolution of

160x 160km. The water column is divided into 6 layers with spatial step of 1Omt. Moreover the velocity field linearly decreases trough the layers (fig.3).

-+ 25cmJs -+ 6.25cmIs -+ 0.78 cmls

Figure 3: Velocity fields in the l", 3rdand 6' layers.

4 Preliminary results

Normalized concentration values are considered and it is assumed that the water depth and diffusion coefficients remain constant throughout the plume. Several configurations are considered, including surface hscharges offshore of three sediment class sizes: fine silt, coarse silt and sand. The source of the surface release is in the point (h = 13O.715; cp = 41'. 169) as reported in figure 3. The sediment size classes and settling velocities are shown in the table 1 as reported in USER'S MANUAL FOR CORMIX (httu:/lwww.co~-mix.info/)

Table 1: Particle Size Class and Settling Velocities

Sediment Size Class Particle Size (pm) Settling Velocity (ds) Sand >62 320

Coarse Silt 16-62 6.28 Fine Silt 3.3-16 0.394

Fine silt: the first results simulate discharges offshore of fine silt that is the principal sediment component in the area, including settling velocity of 0.394 mmls corresponding to a size of 3.3-16pm.

130 Water Pollution VII: Modelling, Measuring and Prediction

Figure 4: dispersion and sinking process of fine silt discharged at the surface

after lsec, l h, 3h, 6h and 10h along the lst, the 3rd and the 6th layer

As reported in fig.4, the fine silt plume released in surface will move from the point of discharge above all by two mechanisms: advection by currents; diffusion by turbulence and in a smaller part by settling. In fact only after 6 hours the 31d layer is included and after 10 hours a little quantity of the tracer reaches the bottom. The residence time are shown in fig.5a-b, where are represented, respectively, the total mass integrated over the whole water column and the total mass trend in each layer

Ctot Ctot

mm 'm *m "" '"" Time (h)

Figure 5: (a) total mass discharged normalized and vertically integrated; (b) total mass in each layer

The total mass remain in the basin for 2.5 hours when the tracer reaches the boundary and the slope in the first layer increases (fig.5b), after 3hours the 2nd and partly the 31d layer are included, but the major part of the substance leaves the basin through the first layers.

Water Pollution VII: Modelling, Measuring and Prediction 131

Coarse silt: subsequently we consider as matter the coarse silt, with settling velocity of 6.28ds corresponding to a size of 16-62pm.

*- ++ **a *- -- / ------A------m~ *- -- P -e -- -- *- - / ------*- -- -.-- ..------..- -

Figure 6: dispersion and sinking process of coarse silt discharged in the surface

after 1800sec, lh, 2h, 3h and 6h along the Ist, the 3rd and the 6" layer

In this case the dynamic of the plume includes the three separate mechanisms: advection by currents; diffusion by turbulence and settling. The tracer doesn't reach the boundary because it sinks completely at the bottom after 6 hours (fig.7b)

Time (h) Time (h)

Figure 7: (a) total mass discharged normalized and vertically integrated; (b) total mass in each layer

Sand: at least it is represented the discharge of sand with size greater than 62 pm with a settling velocity of 320mrnls

132 Water Pollution VII: Modelling, Measuring and Prediction

Figure 8: dispersion and sinking process of sand discharged in the surface after 1Ssec, lmin and 15min along the l st, the 3rd and the 6th layer

In this case neither advection nor diffusion processes are pointed out. After just lminute the sediment includes 60mt of depth and after 15 minutes it is completely at the bottom.

Time (min) Time (min)

Figure 9: (a) total mass discharged normalized and vertically integrated; (b) total mass in each layer

In fig.9a-b is remarked that material coarser than sand may be assumed to settle virtually immediately quite apart from the depth and on water body current velocities (flushing time).

Moreover in fig.9a it is shown that the model verifies the mass conservation while the numerical validation has been reported in Riccio [3] and Grieco [4].

Summary

In this paper a numerical multi-layer model, simulating dispersion processes of matter suspended, has been developed and applied to the Gulf of Gaeta. It has been used an Eulerian approach, based on the integration of the advection- diffusion-sinking equation. A process study has been realized including surface discharges offshore of three sediment class sizes: fine silt, coarse silt and sand.

The velocity field, carried out from measurements from Dello Stendardo Cape to Garigliano River on the February 2002, reveal a longitudinal south-eastward transport with mean surface current of order 20-30cmIs which probably is the

transport with mean surface current of order 20-30cm/s which probably is the cause of the erosion of two areas: Vindicio e S.Janni beaches (Formia) and Scauri (Minturno). Moreover in this littoral zone a sandy reserve stands out at l lKm offshore that could be utilized for the restore of this area, so 6 layers of

l0mt are considered in the numerical model with the velocity field decreasing along the column water. The results show the time taken for sediment to set out of suspension that is dependent on characteristics of the receiving medium such as water depth, the viscosity, the density and the turbulence of and of the sediment itself, such as the grain size and the density (it is not considered the shape of the sediment). In particular large low-density structures, such as fine silt, can remain in suspension for quite a long time, in our results for 10h covering 3600- while relatively large and heavy particles, like sand grains, rapidly sink to the bottom (in fraction of hour). At last, according to this diagnostic study, with similar pattern of currents the Posidonia meadows, which are present on the bottom less than 35mt, are not included in the transport/sedimentation processes that are taken up to offshore areas. In conclusion, the idealization results of the model are applicable and transferable to other regions and scenarios with a realistic parameterization, also in the case of a more complex vertical flow profile.

References

[l] Schiesser W. E., The numerical method of lines integration of partial differential equations, Academic Press, 1985. [2] Hundsdorfer W., Koren B., van Loon M. and Verwer J.G., A positive finite- difference advection scheme, J. Comput. Phys., pp. 117,3546, 1995

[3] Riccio A., Reti di reazioni chimiche e fotochimiche interagenti con processi diffusivi e convettivi, tesi di dottorato in scienze chimiche, Napoli, 1987. [4] Grieco L., Processi di dispersione nel GoEfo Di Napoli, tesi di laurea in Scienze Nautiche, Napoli, 1998. [S] Okubo A., Oceanic diffusion diagrams, Deep Sea Research, Pergamon

Press, vol.18, pp.789-802, 1971. [6] Jiang J., Mehta A.J., Fine-Grained Sedimentation in a Shallow Harbor, Journal of Coastal Reseaxch, 17(2), pp.389-393,200 1 [7] Mann KH., Lazier JR, Dynamics of Marine Ecosystems: Biological- Physical Interactions in the Oceans, 2nd Edition (1996)