A simple model for showing effects of geometry on the ocean tides

There is a need for a simple model to show effects of ocean shape on the tides and, in particular, to show how the Atlantic tides interact with those of the Southern Ocean. In response to this need, the Atlantic and Southern Oceans are here represented by narrow canals which meet in a T-junction. Analytic solutions for this geometry are easily obtained. Rotation effects can be included by calculating the second terms in an expansion in a small parameter proportional to the widths of the canals, and this can produce a realistic configuration of cotidal lines. The solution is studied in a two dimensional parameter space, the two parameters corresponding to the ocean depth and the mean latitude of the Southern Ocean. The solution is very sensitive to parameter values near the resonance line, but also depends very much on position in parameter space relative to a special point on the resonance line where the equilibrium tide is orthogonal to the resonant free oscillation. With a small friction, solutions on one side of this point generally give southward propagation of tides in the Atlantic, while northward propagation is generally obtained for parameter values on the other side. The effect depends on the direction in which the phase of the free tide is shifted relative to that of the direct tide. Useful conclusions about some old controversies can be made in the light of these results.