Directly multimoded two-flow long surface waves

The purpose of this study is to reduce in a relatively direct fashion the general two-dimensional linear hydrodynamic equations, for long surface waves in a rotating lossy two-port basin, to a set of coupled ordinary differential equations governing the multimode amplitudes of two counter-flowing wave trains between the ports of the basin. A relatively direct and novel reduction is made of the long wave hydrodynamic partial differential equations into sets of coupled ordinary differential equations governing the two-flow components of wave elevation in natural water basins. These basins have two ports, arbitrary coastlines, are rotating as parts of the rotating earth, and exhibit bottom friction.