Theoretical study of unstable waves in the rapids of the river

概要

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The interesting phenomena of surface waves in the rapids of the river will be easily observed at the waterside. Particularly, it has been pointed out that only the periodic component of the waves generated at the rapids will propagate to the waterside of the down-stream pool. In order to elucidate their generating mechanisms, the simplified equations of motion, which involve the terms of the dispersion, Manning's resistance law and the eddy viscosity, are analysed by using perturbation methods and numeical calculations.<BR>The linear and the nonlirear stability the orys how that down-going waves become convectively unstable and their equilibrium amplitude does not exist at the low values of the roughness parameter. The critical Froude number Frcr and the conesponding frequency and wavenumber of unstable waves are also determined as a function of the roughness parameter. In addition, it is revealed that the scaling of the KdV-type, which is the long-wave approximation, yields also the KdV equation, but its dispersion term comes fromt he eddy viscosity and its solution expresses the kinematic wave.<BR>Furthermore, the waves induced by the bottom topography, whose slope is given by a sinusoidal or a step function, will be investigated numerically by spectral methods.
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