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A Time-Domain Analytic Solution of Flow-Induced Undular Bores

In this study, the problem of surface waves induced by water flow in a flow channel was investigated. The mathematical model based on the potential wave theory was established, and a new analytic solution to the corresponding initial and boundary value problem was proposed. To confirm our analytic solution, the mathematical model was applied to simulate experiments conducted in a flow channel in the laboratory. Using our analytic solution, water surface elevations and flow velocities at certain locations in the channel were compared with experimental results. Comparisons between our analytic solution and experimental results confirmed our theory that amplitudes and propagating phases are in very close agreement. Our analytic solution can be used to calculate variations in pressure and velocity along the water depth, which are expensive to calibrate and obtain in experiments. Although our analytic solution was established based on linear theory, it is very practical for applications studying the basic properties of surface elevation, velocity, and pressure of the flow field induced by water current both in space and time.