Description.

The Río de la Plata is located on the East coast of South America, approximately between $34^\circ$ through $36^\circ$ South Latitude and $54^\circ 50'$ through $58^\circ 30'$ West Longitude, being a limit between the República Oriental del Uruguay and the República Argentina. Its axis runs on a NW-SE direction being approximately 280 km length. Its surface is about 35.000 km² and its width varies over 2 km at Punta Gorda in the North (Nueva Palmira in figure 8.2) and about 220 km at its mouth (the line that goes from Punta del Este in Uruguay to San Clemente in Argentina, same figure).

Río de la Plata singularity is based on its micro-tidal astronomic regime, with a few centimeters amplitude, opposed to the high relevance of the meteorological surges, which have a lifetime of several days and up to 3 meters high-tide and flood. In other shallow-water scenarios of the world, like in North hemisphere estuaries, the prevalent tide is the astronomic instead, which has semi-diurnal or diurnal periodic behavior and amplitudes that reaches several meters.

The above described Río de la Plata particular behavior may be explained by the proximity of two amphidromic points^11.1 (Cartwright et al., 1991; Ray, 1993; Schwiderski, 1983) in the South Atlantic region. Therefore, the meteorological tide effect has fundamental importance in the region, it depends on wind predictions for the simulation, and introduces further complexities, like the long duration of the the events, which must be accomplished in the modeling.

The significance of PTidal code application in the region resides fundamentally in its capability to challenge the above described peculiar behavior while producing results in real time, to allow its used as a predictive tool.

In accordance to the amplitudes of the South Atlantic amphidromic systems, described in Schwiderski (1983) and Ray (1993), the incidence of the main astronomic wave fronts over the Río de la Plata are predominately from the South. For this reason the M₂ surge front enters into the Río de la Plata from the South arriving at La Paloma port, on the Uruguayan coast, approximately 2 hours after going past San Clemente port, over the Argentinean coast (see figures 8.2 and 8.2).

At the South border of the computational domain the astronomic wave has been forced, following the above basic assumption. A calibration process has been performed, comparing model results and actual waves as in figure 8.2, adjusting, along this boundary, the wave amplitude and phase.

The East section of the Oceanic Boundary demanded the use of the low reflecting BC condition, introduced in Section 4.4.3, to allow the reflected surges inside the calculus domain to go out through it. This implementation has been motivated by the ocean amphidromic systems observation as well.

At the North, the fresh water inflow through Uruguay and Paraná Guazú - Las Palmas rivers is simulated. Uruguay river, with a mean flow of 3860 m³/s, discharges straight from the North. Paraná river branches discharge from the NW through its delta system, which has been simulated dividing it into: 12.780 m³/s inflow for the Guazú branch and 1.950 m³/sfor the Las Palmas branch (see figures 8.2 and 8.2).

The bottom profile has been interpolated (Pankratov, 1995; Watson, 1994) into the grid points from digitized data of several navigation charts (Cartas de Navegación del Río de la Plata, 1995).

Physical values employed in the modeling are: $\rho_a = 1 \quad kg/m^3$, Z₀=0.001 m, $\phi = -35^\circ$, $\omega = 2 \pi / (24 \times 3600)$ rad/s.

Several values for the wind stress coefficient were tested. The value which gave best results in the storm surge modeling was $C_d=2.4 \times 10^{-3}$.

For a grid size of 1000 m the $\varepsilon$ value that gave better results in the simulation was 800 m²/s. The time step was selected as 1 minute for the explicit-implicit code and 2 minutes for the fully-implicit code.