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A set of differential equations does not mean anything unless appropriate boundary conditions are specified. The number of boundary (or initial) conditions is closely related to the behaviour of characteristics if the system is hyperbolic. The SWE are hyperbolic if you do not take lateral friction into account. You can find the relevant theory in Courant & Hilbert (1962). It says first of all that the region of interest should be enclosed by a boundary with no holes in it. Such boundaries can obviously be coastlines, but if you take a region covering part of the sea, you also have an “open” boundary which is artificial in the sense that it is not a physical boundary: it is just a line drawn on the map.
KeywordsReflection Coefficient Froude Number Boundary Data Normal Velocity Potential Vorticity
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