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Oil spills can generate multiple effects in different time scales on the marine ecosystem. The numerical modeling of these processes is an important tool with low computational cost which provides a powerful appliance to environmental agencies regarding the risk management. In this way, the objective of this work is to evaluate the influence of a number of physical forcing acting over a hypothetical oil spill along the Southern Brazilian Shelf. The numerical simulation was carried out using the ECOS model (Easy Coupling Oil System), an oil spill model developed at the Universidade Federal do Rio Grande—FURG, coupled with the tridimensional hydrodynamic model TELEMAC3D (EDF, France). The hydrodynamic model provides the current velocity, salinity and temperature fields used by the oil spill model to evaluate the behavior and the fate of the spilled oil. The results suggest that the local wind influence is the main forcing driven the fate of the spilled oil, and this forcing responds for more than 60% of the oil slick variability. The direction and intensity of the costal currents control between 20% and 40% of the oil variability, and the currents are important controlling the behavior and the tridimensional transportation of the oil. On the other hand, the turbulent diffusion is important for the horizontal drift of the oil. The weathering results indicate 40% of evaporation and 80% of emulsification, and the combination of these processes leads an increasing of the oil density around, 53.4 kg/m3 after 5 days of simulation.

The outpouring of oil and derivatives on the marine ecosystem is an important subject to be considered by the modern society, since the oil is composed by toxic substances that exposed on the environment can create chronic effects [

The Southern Brazilian Shelf (Figures 1(a) and (b)) presents high susceptibility for eventual accidents regarding the oil spill, since nowadays there is an intense oil transportation in this region due to the Rio Grande Harbor, the Transpetro Waterway Terminal (Petrobras) and the Riograndense Oil Refinery S/A. The major part of the transportation activities identified in this region occurs on the estuarine environment of the Patos Lagoon and near the adjacent coastal region. In 2003 year almost 3000 ships were moved and in during 2008 year more than 60,000 tons of oil was transported in the Rio Grande Harbor (www.portoriogrande.com.br).

The oil spill in estuaries is worrying because these are ecological and economically important environments. The estuaries retain a large amount of the spilled oil, increasing the contamination effects. Therefore, the estuaries are the environments that present the major sensibility degree according with the scales used in the oil sensitivity maps.

According to the Brazilian legislation, the numerical simulations of spilled oil must define the area of indirect influence of this activity, in which all the environment diagnostic is based. In this sense, the diagnostic defines and simulates scenarios allowing the development of

strategies for an oil spill accident in the ocean into the emergency plane of the companies. Therefore, the objective of this paper is to investigate the effects of different physical forcing controlling the behavior and the fate of an oil spill near the Patos Lagoon entrance.

The numerical model TELEMAC3D (EDF—Laboratoire National d’ Hydraulique et Environnement of the Company Eletrecité de France) has been used for tridimensional hydrodynamic simulations. This model solves the Navier-Stokes equations using finite element techniques for spatial discretization. It considers the free surface variation for incompressible fluids and considers the Boussinesq approximation in order to solve the momentum equations [

The ECOS (Easy Coupling Oil Model) has been developed through techniques of modular programming between object-oriented paradigm, which allows a better structuring and control of the libraries related to the subprograms and functions. This type of organization allows the compilation of each module apart, saving computational time, so that the reutilization of the functions is facilitated. The model uses a coupling interface, which contains all the necessary information to be shared by the oil and hydrodynamic model. The processes of what the oil is subject when arrives at the environment, such as spreading, turbulent diffusion, evaporation, dispersion and emulsification are implemented.

This section quickly describes the mathematical formulations used by some actual oil models and those used by the ECOS model developed at FURG. This model treats the oil like discrete particles using Lagrangian approximation to evaluate the tracer (particles) proprieties during time.

The tracer trajectory is evaluated considering the oil like a large number of particles which moves independently in water. The tracer velocities are interpolated from the current velocity in each node of the hydrodynamic numerical domain (

The final tracer position depends on four different factors: 1) Current velocity; 2) Wind velocity; 3) Spreading effect; and 4) Turbulent diffusion. In this work, the effects associated with the slick drift are described in the following sections.

In this work, all the effects which are independent from the physical-chemical effects are considered like advective forcing. In these classes are evaluated the drifting driven by the current and winds, and also the vertical transport due to the buoyancy associated with the difference of density between the oil and the water. The zonal (U), meridional (V) and vertical (W) components of the velocity are calculated by the Equations (1)-(3), respectively. Whereand are the coefficients of influence of the currents and winds.

The particle buoyancy law (Equation (4)) is based on a modified stokes law for the oil according to [11,12]. In

this formulation is the vertical particle velocity.

where: g is the gravity acceleration, ρ_{o} is the oil density at the initial time t_{o}_{,} ρ_{w} is the average salt water density and ν_{w} is the water viscosity.

Maximum and minimum droplets sizes are evaluated through [

This formulation uses wave energy (σ) and wave period (ω), at this moment the model uses constants averaged values for this parameters.

All the processes that depend on the oil physical-chemical characteristics are considered as diffusion processes. This class fits spreading and turbulent diffusion, and both processes are function of the tensions in the oil-water interface. In this way, these processes are represented through “random-walk” techniques.

The spreading is a horizontal expansion effect due to the different superficial tensions between the water and the oil. This represents a force balance between gravity acceleration, inertia, viscous and superficial tensions. This process is very important during initial moments after spill.

The algorithm used to evaluate the oil spreading determines the random velocities U_{d} and V_{d} uniform distribution in the range [−U_{r} + U_{r}] and [−V_{r} + V_{r}] (along x and y directions, respectively) proportional to the diffusion coefficients, which are calculated assuming that the Lagrangian tracers spread according with the solution proposed by [_{x} and D_{y} and the interval of the flotation velocity [−U_{r} + U_{r}] and [−V_{r} + V_{r}] are adopted according to [_{x} and D_{y} are calculated according to Equation (8):

The intervals of flotation [−U_{r} + U_{r}] and [−V_{r} + V_{r}] are calculated according to Equations (9) and (10).

The random velocities U_{si }and V_{si} are, therefore, determined by the formulation proposed by [

where R_{1} and R_{2} are random numbers generated from a normal distribution between 0 and 1.

The horizontal turbulent diffusion is evaluated through a modified mixing length turbulence model for the oil spills. Maximum distance that a particle can go from actual (t) position is calculated in Equation (13), equivalent to a traditional mixing length model. Equations (14) and (15) estimate the particle velocities based in a “random walk” method.

4.3. Particle Path Finally, after the definition of all forces acting in a particle, the positions can be integrated in time, by an Euler forward method. Equations (16)-(18) evaluate each particle position during time.

Evaporation is considered one of the most important processes in an oil spill, once it controls the mass balance and can cause about 75% of lost mass according to [

The creation of a mousse, mainly characteristic of this process, occurs due to the incorporation of water in oil slick through the polar components of the oil. Equation (20) represents the water incorporation in oil according to [

This process is very important in the oil spill modeling, once the buoyancy of the oil particles is determined. It causes the sinking of the oil if the water density is lower than the oil density. In a quickly view, during the evaporation process occurs mass lost, while during the emulsification process occurs mass gain of the oil slick. Therefore, the balance of these processes defines the final oil density. Equation (21) evaluates the oil density according to [

The ECOS model has been directly coupled to the TELEMAC3D source code (see [

Time series of oceanographic data are used as boundary conditions. The boundary conditions currently implemented include time series of river discharge, water levels, salinity, temperature, current and wind velocity. The river discharge was obtained by ANA (Agência Nacional de Águas) website. Salinity, temperature, current velocity and water levels were obtained by the global predict model OCCAM (Ocean Circulation and Climate Advanced Model). Wind and air temperature data were provided for the NOAA page (National Oceanic & Atmospheric Administration).

Nowadays, the oil model considers an accidental punctual spill (see

In this work, the initial conditions of the oil model are:

area is defined at the end of this phase with the beginning of the gravitational-viscous phase in Equation (22).

In order to accomplish the objectives, two simulations were carried out. The first simulation (simulation 1) includes all the physical forcing the oil slick dynamics. On the other hand, the second simulation (simulation 2) was carried out without consideration of the local wind influence acting over the oil slick. The results regarding only the hydrodynamic processes are not analyzed in this work, because an extensive description of hydrodynamic processes along the Southern Brazilian Shelf can be found in: [20,22] and [6-9].

Results for the temporal evolution of the tracers are presented in

Through the analysis of the wind direction in

Results without the local wind influence acting over the oil slick are presented in

The oil slick behavior and its further destination are strongly influenced by the coastal wind driven circulation pattern with the alongshore drifting to the south region due to northeastern winds. This behavior is consistent with results obtained by [6-9] among others, for the coastal circulation near the Patos Lagoon entrance.

In order to quantify the contribution of the local wind effect as determinant factor controlling the oil slick behavior, a time series analysis is presented.

The second major contribution, controlling from 20% to 40% of variability, is provided by the coastal currents which drives the oil initially on the direction of the superficial currents, except by the particles that suffer process of sinking according with the following tridimensional circulation pattern developed. The turbulent forces act in a secondary way responding for less than 20% of variability generating a horizontal disintegration of the oil slick during all the period of simulation. The spreading component decreases very fast, being active on the first hours of simulation. However, this component dominates the initial disintegration of the slick.

During the first 2 hours of simulation, the currents dominate the spreading of the oil spill because of the time response associated with the local wind influence acting over the oil slick. In addition, during periods of changing in wind direction (about 10 hours of simulation), the costal currents turn to dominate the behavior of the oil slick.

The direct correlation between the displacement of the oil slick and the local wind influence is observed and the most important cycles occur from 12 to 16 hours, following the short time variability of the winds over the study region. The spectral content and the correlation between these time series (

The analysis of the local power spectrum (

On the analysis of the tracer trajectory there is not enough information to explain the oil spill behavior. Therefore, it is necessary to consider the analysis of the scalar properties, such as evaporation and emulsification that act directly on the oil density.

The behavior of the emulsification is corroborated by the experiments proposed by [

The increase of the oil density makes it reach a density very close to the salt water, which causes a balance of phases enhancing the importance of the effects controlled by the tridimensional circulation causing processes such as vertical dissolution and sedimentation of the spilled oil.

The principal conclusions obtained in this study are:

• Wind acting over the oil slick is the most important forcing controlling its behavior and further destination. This forcing mechanism responds for more than 60% of the oil variability during almost all the time.

• The winds from the Southern (Northern) quadrant induce the movement of the oil slick directly to the coast (offshore).

• Intensity and direction of the coastal currents control between 20% and 40% of the oil variability during the simulated period. This forcing is important for the vertical distribution of the oil along the water column. The diffusive forcing represents less than 20% of the variability and it has secondary effect acting mainly on the horizontal dispersion of the oil slick.

• During 120 hours of simulation about 40% of the oil evaporates and 80% of the oil emulsifies. The combination of these effects generates an increase of 53.4 kg/m^{3} on the density, showing the magnitude of the mixture and the aging processes.

• Simulation without the consideration of the winds on the oil slick is slacking realistic because the oil slick does not reach the coast any moment even by the influence of favorable winds. Besides, after 48 hours of simulation, the aging processes are dominant and, in some way, it commits the results obtained by the spreading of the oil slick after this period.

The authors thank to the Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPQ and the Agência Nacional do Petróleo—ANP for the fellowships

provided which helped the development of this work. The authors still thank to the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul—FAPERGS for partially support this work (Process: 11/1767-4, Process: 1018144 and Process: 179912-3). Further acknowledgements go to the Brazilian Navy for providing detailed bathymetric data for the coastal area, to the Brazilian National Water Agency (ANA) and the National Oceanic & Atmospheric Administration (NOAA) for supplying the fluvial discharge and wind data sets, respectively, and to the EDF for providing the TELEMAC System to accomplish this research.