Numerical tidal models with unequal grid-spacing

Abstract

A two-dimensional alternating-direction implicit numerical tidal model with unequal grid-spacing is developed and successfully tested. The method is essentially an extension into two dimensions of a one-dimensional implicit method in which tide heights and flow rates are evaluated on the same cross-sections, an approach which permits a river to be schematized into a number of sections of differing lengths. The two-dimensional scheme gives the user considerable control over the density of the computation points in a region by virtue of the fact that heights and depth-mean currents are evaluated midway between points of intersection of a grid constructed from orthogonal lines, the spacing between which may be chosed at will. The method is applied initially to the Irish Sea using a grid of constant spacing. The effects of increasing time step and friction on stability and accuracy are investigated, and the model is proved to be unconditionally stable. The results match those of previous investigators, and some new information on the M₂ currents of the region is obtained. The second application of the model is to a 'rectangular' North Sea, a favorable comparison being obtained when the region is schematized by two grids of equal and unequal spacing. Finally, the model is applied to Cook Inlet, Alaska, a region of complexity sufficient to warrant the use of a scheme possessing the unequal grid-spacing feature. Satisfactory results are obtained after tuning the model by adjustment of the friction coefficient. Movie films were made in order to conceptually clarify the tidal behaviors of the Irish Sea and Cook Inlet. Each film shows as functions of time, perspective views of the sea surface, and current vectors superimposed on a contour map of the sea surface.