The numerical simulation of tide and storm surge propagation in two-dimensional space using the method of characteristics
The non-linear hyperboIic partial-differential equations governing long-wave propagation in two spatial dimensions are postulated. Through the method of characteristics, specific conditions are developed for integrating the Iong-wave equations. By introducing finite difference approximations to the characteristic conditions, an explicit numerical scheme is developed as an alternative to more standard finite differencetechniques. The modifications required at the open and closed boundary points are of particular importance and lead to a 45° characteristic numerical scheme. A practical assessment of stability and consistency criteria associated with the numerical scheme is shown to be important for the successful simulation of free and forced tidal oscillations. Tests with motion prescribed by analytical solutions verify the accuracy of the integration procedure and lead to the correct form of interpolation coefficients. A method of subdivisions is developed for improving the simulation of free wave oscillation in a closed basin of trapezoidal profile. Analytical solutions for steady and unsteady wind surges are used to examine the effect of introducing wind stress terms into the numerical scheme. A practical evaluation of the scheme is accomplished by simulating tidal propagation in the Clyae sea area. Tidal motion in this region is highlighted by the existence of an amphidromic point. Data for the model, provided by a tidal survey, confirm certain values of range and phase given in the Tide Tables (1979). Two separate surge events are simulated in the Clyde sea area. The relative size of each surge component and the interaction between tide and surge are established. The forms of the surges and the meteorological conditions required for their propagation into the Clyde sea area are also assessed. Finally, a west coast shelf model is developed to overcome the problem of specifying the external surge as a boundary condition.