Logarithmic matching and its applications in computational hydraulics and sediment transport

dThis study presents an asymptotic matching method, the logarithmic matching. It states that for a complicated nonlinear problem or an experimental curve, if one can find two asymptotes, in extreme cases, which can be expressed as logarithmic or power laws, then the logarithmic matching can merge the two asymptotes into a single composite solution. The applications of the logarithmic matching have been successfully tried in several cases in open-channel flows, coastal hydrodynamics and sediment transport such as: 1) the inverse problem of Manning equation in rectangular open-channels, 2) the connection of different laws in computational hydraulics, 3) the solution of linear wave dispersion equation, 4) criterion of wave breaking, 5) wave-current turbulence model, 6) sediment settling velocity, 7) velocity profiles of sediment-laden flows, and 8) sediment transport capacity. All these applications agree very well with numerical solutions or experimental data. Besides, it is pointed out that there are several other cases where the logarithmic matching has potential applications.