Modelo Matemático de los Fenómenos que Modifican el Oleaje. Aplicado a las Obras de Protección de la Central Núcleo Eléctrica Laguna Verde (CNLV)

Abstract

In projects of great importance in the maritime hydraulic, in our country, is immersed the wave phenomena that propagates from deep water to shallow water; this affects in the structures to minimize the sediments transport on the coast, as well as protecting our Mexican ports, for the exchange of merchandise in other countries and our territory, being currently one of the more economical transportations. However, these type of structures need an adequate study and analysis for planning and construction, because if it is not carried out adequately, there can be important agitation and transportation problems of sediments in the port precinct, generating great maintenance costs for its correct operation. This document presents the numerical modeling of the Berkhoff’s equation (1972) in its elliptic form, known as the mild - slope equation. The components equation are deduced to the wave phenomena with the lineal theory, harmonic waves, and effects due to currents and describe the propagation of a wave in the periodic free surface and of finite amplitude over complex bathymetry, where its deformation approaching to low depth zones and obstacles presents the refraction, diffraction and reflection phenomena. The solution of the Berkhoff ‘s equation is worked and expressed in function of the wave flow rate in its components x and y, this by means of a time implicit scheme through finite differences. Systems of tridiagonal matrices are built for the flow rate on the horizontal plane and a pentadiagonal matrix to solve the free surface equations in function of the flow rate calculated previously. A Staggered-Cell grid was employed, where the flow rate, velocities and other variables are located on the faces and the free surface is located on the center of the cell. The programming of the wave phenomena numerical modeling was carried out with a model developed in MATLAB of the elliptic approximation of the Berkhoff’s equation. Its application was aimed to see the wave phenomena behavior on the protection structures (breakwater) of the Laguna Verde Nuclear Power Station (Central Nucleoeléctrica de Laguna Verde), placed in Veracruz State, Mexico. Another application of the model, the variation of the thermal plume is presented considering the wave phenomena (regular) and the influence of the atmospheric temperature over the free surface to show that these variables are an incident factor in the temperature variation inside the precinct. In comparison with some examples developed by means of mathematical modeling, is possible to conclude that the results obtained in the wave module are satisfactory