Theoretical study of unstable waves in the rapids of the river
PROCEEDINGS OF HYDRAULIC ENGINEERING
Theoretical study of unstable waves in the rapids of the river The interesting phenomena of surface waves in the rapids of the river will be easily observed at thewaterside. Particularly, it has been pointed out that only the periodic component of the waves generated at the rapidswill 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
... sistance law and theeddy viscosity, are analysed by using perturbation methods and numerical calculations. The linear and the nonlirear stability theory show 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 from the eddy viscosity and its solution expresses the kinematic wave. Furthenmote, 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.