Abstract
When a forcing moves in a shallow channel at a velocity near the phase velocity for linear long waves, energy cannot escape from the forcing at the linear group velocity and nonlinear effects become important in describing the resulting flow. This flow is termed resonant or transcritical. It has been found both experimentally and numerically that large amplitude upstream propagating waves are generated by the forcing. These waves are straight crested, even though the forcing is two-dimensional. It is shown that these upstream waves become straight crested due to geometrical effects aided by the presence of side walls. Using energy conservation, approximate values of the amplitude of the upstream waves are obtained which are compared with recent experimental and numerical results.
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Smyth, N.F. Formation of one-dimensional waves for resonant flow in a channel. PAGEOPH 133, 619–633 (1990). https://doi.org/10.1007/BF00876225
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DOI: https://doi.org/10.1007/BF00876225