**5. Numerical modeling**

The propagation of the tidal flow in estuaries is a complex free surface problem. It is unsteady oscillatory and therefore may have reversal flow that is not uniform. The equations governing the flow (conservation of mass and movement) are not linear due to friction, the spatial variations velocity and changes in the dimension of the estuary (Gallo, 2004, Cunha, 2008). Thus, to resolve the hydrodynamic in general and the propagation of the tidal estuary, taking into account this complexity, it is necessary to use numerical models to represents the average flow.

According to Versteeg & Malalasekera (1995) a turbulence model can be considered a computational procedure applied to close the system of equations used to represent the average flow, and calculations applicable to a variety of generic problems regarding flow dynamics. The authors state that one of the models most useful in solving the set of equations to be solved for the transport of Reynolds stresses is the *k-* model. The standard *k-ε* model presents two equations, one for *k* and one for based on our understanding of the processes that cause relevant changes in these variables. The turbulent kinetic energy *k* is defined as the variance of velocity fluctuations and is the dissipation of turbulent kinetic energy (the rate at which turbulent kinetic energy is dissipated in the flow). *k-* turbulence model and the SST (Shear Stress Tensor - a more complex variant of the *k-* model) were used respectively for closing the Reynolds equations (Cunha, 2008; Pinheiro & Cunha, 2008). Cunha (2008) and Pinheiro & Cunha (2008) conducted two case studies with numerical models using the software CFX/ANSYS 1) coastal area on the coast of the city of Macapá, and 2) the Matapi River, near the Industrial District of the city of Santana (0° 0'32.53"S, 51°12'7.43"W) (Fig. 3a and 3b). In both cases, the objective was to study the dispersion behaviour of pollutant plumes into surface waters in the estuary of the Lower Amazon and their behaviour during a semi-diurnal tidal cycle.

Fig. 3. Pre-processing within a CFX (Computational Fluid Dynamics) study of the dispersion of pollutants in the estuarine zone next to Macapá: a) Macapá and Santana Coast; b) Matapi River (point 8 in Fig. 3a), near the Island and Industrial District of Santana-AP.

The propagation of the tidal flow in estuaries is a complex free surface problem. It is unsteady oscillatory and therefore may have reversal flow that is not uniform. The equations governing the flow (conservation of mass and movement) are not linear due to friction, the spatial variations velocity and changes in the dimension of the estuary (Gallo, 2004, Cunha, 2008). Thus, to resolve the hydrodynamic in general and the propagation of the tidal estuary, taking into account this complexity, it is necessary to use numerical models to represents the average

According to Versteeg & Malalasekera (1995) a turbulence model can be considered a computational procedure applied to close the system of equations used to represent the average flow, and calculations applicable to a variety of generic problems regarding flow dynamics. The authors state that one of the models most useful in solving the set of

processes that cause relevant changes in these variables. The turbulent kinetic energy *k* is

used respectively for closing the Reynolds equations (Cunha, 2008; Pinheiro & Cunha, 2008). Cunha (2008) and Pinheiro & Cunha (2008) conducted two case studies with numerical models using the software CFX/ANSYS 1) coastal area on the coast of the city of Macapá, and 2) the Matapi River, near the Industrial District of the city of Santana (0° 0'32.53"S, 51°12'7.43"W) (Fig. 3a and 3b). In both cases, the objective was to study the dispersion behaviour of pollutant plumes into surface waters in the estuary of the Lower Amazon and

Fig. 3. Pre-processing within a CFX (Computational Fluid Dynamics) study of the dispersion of pollutants in the estuarine zone next to Macapá: a) Macapá and Santana Coast; b) Matapi

River (point 8 in Fig. 3a), near the Island and Industrial District of Santana-AP.

based on our understanding of the

is the dissipation of turbulent kinetic

model. The standard

turbulence

model) were

equations to be solved for the transport of Reynolds stresses is the *k-*

energy (the rate at which turbulent kinetic energy is dissipated in the flow). *k-*

model and the SST (Shear Stress Tensor - a more complex variant of the *k-*

*k-ε* model presents two equations, one for *k* and one for

defined as the variance of velocity fluctuations and

their behaviour during a semi-diurnal tidal cycle.

**5. Numerical modeling** 

flow.

Fig. 4. Velocity and dispersion of pollutants in natural runoff - in the coast of the cities of Macapá and Santana. Representation of a semi-diurnal tidal cycle.

Challenges and Solutions for Hydrodynamic and Water Quality in Rivers in the Amazon Basin 83

In both case studies, despite the sophistication of the numerical analysis, technical advances such as calibration and validation of models are still necessary. The complexity of the process involving modelling steps, proceedings to investigate the aquatic biogeochemistry and hydrometry of large rivers have yet to beovercome in the estuarine region of Amapá.

Fig. 6. Low and rising tides. t = 360 min (6.0 h). a) Velocity; b) Stream line; b) Plume

interaction between the plume of the Amazon River and Atlantic Ocean).

because of the intricate system of channels in the Amazon River.

In the estuarine region of the Lower Amazon River, in the state of Amapá, the measurement of net discharges of large tidal rivers is only feasible with the use of devices such as ADCP to integrate hydrodynamic processes and water quality variables (biogeochemical cycle and

Relevant hydrodynamic parameters such as velocity profiles, stress and identification of background turbulent flow velocity components need to be determined with the aid of modern equipment whose operation must be efficient and economic for hydrometric

Bathymetric analyses, at the scales of interest, have been a difficult hurdle to overcome

The logistics required for experimental studies in large rivers is a major obstacle that has

A major challenge to be overcome in systematic studies of water quality parameters is the generation of local physical parameters, such as rating curves, rates of sedimentation and resuspension of sediments, etc, which are a fundamental input for complex numerical

Concentration.

**6. Conclusions** 

models of water quality.

The main conclusions of this research are:

quantification in complex estuarine environments.

inhibited research interest in this poorly studied area.

Fig. 3a illustrates the pre-processing step for simulation of pollutant dispersion and demonstrates the complex geometrical configuration required to represent the turbulent flow. There are six continuous pollution sources in the cities of Macapá and Santana, from the mouth of the Matapi River (southern area) to the north of the city, the upper area of the figure. The natural flux of flows passes from the bottom (left) to top (far right, in the north and northeast). The continuous point sources of pollutants are represented by red circles along the coast, which represent the main release points of untreated pollutants into the waters in Macapá and Santana cities (Pinheiro & Cunha, 2008). The same representation occur in Rio Matapi indicated by Fig 3b (Cunha, 2008).

Fig. 4 shows the results of the simulations of pollutant dispersal plumes (light blue and reddish margins) during a tidal cycle. These maps show that the plumes tend to stay close to the shore. From left to right (top row) is the initial phase of a simulated low tide (approximately 7 hours). Again, from left to right (bottom row) begins the high tide phase (approximately 5.5 hours). During the tidal cycle it was possible to simulate the complex interactions between hydrodynamics and a coupled scalar (hypothetical pollutant), with an emphasis on the dynamic plumes between mainland Santana and the island of Santana.

Case study 2 (Fig. 5), shows the phases of the dispersion of pollutant plumes (hypothetical tracer) in the Matapi River during a tidal cycle. The flow pattern (streamlines) changes significantly over a period of the semi-diurnal tide. Simulating the dispersal of pollutants indicates a remarkable complexity in the flow, depending on the geometry of the river channel and the timing of the reversal of the tidal cycle.

In Fig. 5, from left to right depicts changes in pollutant plumes during low tide (approximately 7 hours), during a complete semi-diurnal tidal cycle, where the natural flux of the tide flows from top to bottom. The reverse shows the rising tide.

In Fig. 6, from left to right, there are three different flow fields indicated: a) velocity vectors, b) streamlines (paths of constant speeds), c) dispersion pattern of the scalar from two (hypothetical) continuous point sources of pollutants.

Fig. 5. Lines of transient currents in the Rio Matapi: a) low tide at t = 1h, b) end of the ebb at t = 5.5 h, c) reversal of the tide at t = 6h.

In both case studies, despite the sophistication of the numerical analysis, technical advances such as calibration and validation of models are still necessary. The complexity of the process involving modelling steps, proceedings to investigate the aquatic biogeochemistry and hydrometry of large rivers have yet to beovercome in the estuarine region of Amapá.

Fig. 6. Low and rising tides. t = 360 min (6.0 h). a) Velocity; b) Stream line; b) Plume Concentration.
