Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented

Process of Expropriation of Buildings for the Construction of the New Dock of the Port of Cartagena (Spain) in the 18th Century

The need of the Bourbon monarchy to build a Naval Base in the Bay of Cartagena (Spain) during the eighteenth century, implied performing various actions on the environment which allowed the construction of the new dock. One of the priority actions was the transformation of the watershed of the streams that flowed into Mandaraches´s sea. For this reason, a dike was designed and constructed in the northern part of the city. The design of this great work, which was designed as a fortification of the city, was subject to considerable uncertainties. Its proximity to the city involved the demolition of several buildings in the San Roque´s neighborhood. The greater or lesser number of affected buildings and the value of the just indemnification for the expropriation of them, become decisive factors to determine if the work was viable for the Royal Estate or not.

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented.

Runup variability due to time dependence and stochasticity in the beach profiles: two extreme cases of the Spanish coast

Equations for extreme runup worked out from several experimental studies are compared. Infragraviatory oscillations dominate the swash in a dissipative state but not in intermediate - reflective states. Therefore two kinds of equation depending on either significant wave height, H-0, or the Iribarren number, xi(0), should be used. Through a sand bed physical model with a uniform sand bed slope, equations are proposed for both beach states, and results are compared with precedent field and physical model experiments. Once the equations are chosen, the time-longshore variability in a medium - long term time scale of the foreshore slope is evaluated in two extreme cases relating to the Spanish coast. The Salinas beach on the North coast (Bay of Biscay) displayed a permanent dissipative beach state with small variations in the beach foreshore slope both along the shore and in time, so foreshore slope deviations in a medium-long term period were irrelevant and extreme runup is predicted with the wave height worked out from the design return period. Peniscola beach on the East coast (Mediterranean sea) displayed an intermediate state. If only time variations are analysed, variations in determining extreme runup are irrelevant. In contrast, significant differences were found when the longshore variations were studied in this Mediterranean beach.