Wave hierarchies in alluvial river flows
- 1 March 1990
- journal article
- research article
- Published by Informa UK Limited in Geophysical & Astrophysical Fluid Dynamics
- Vol. 51 (1), 167-194
- https://doi.org/10.1080/03091929008219855
Abstract
The long wave equations governing the flow in alluvial rivers and channels are considered. The linearized equations are re-cast in the form of a single equation of wave hierarchy type as discussed by Whitham (1974). The dynamic and kinematic waves are of third and second order respectively. Behaviour at the wave fronts is considered and a roll-wave type instability is revealed. For stable flow, the theory is used to make both qualitative and quantitative predictions in the areas of short and long term floods, tidal waves and channel dredging. The non-uniformity in the quasi-steady theory on bedform development [see, for example, Reynolds (1985)] as the Froude number, F, approaches unity is also discussed, and appropriate scalings are obtained to derive a theory which remains valid when F ∼ 1.Keywords
This publication has 10 references indexed in Scilit:
- The development of a bedform disturbance in an alluvial river or channelZeitschrift für angewandte Mathematik und Physik, 1988
- Nonlinear solution of aggradation and degradation in channelsJournal of Hydraulic Research, 1987
- Turbulent and inertial roll waves in inclined film flowPhysics of Fluids, 1987
- Comparison of MOBED and HEC-6 river flow modelsCanadian Journal of Civil Engineering, 1985
- Aggradation in rivers due to overloading - analytical approachesJournal of Hydraulic Research, 1985
- On roll waves down an open inclined channelProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- DIFFUSION MODEL FOR AGGRADING CHANNELSJournal of Hydraulic Research, 1983
- Waves on the erodible bed of an open channelJournal of Fluid Mechanics, 1965
- Mathematical solution of the problem of roll‐waves in inclined opel channelsCommunications on Pure and Applied Mathematics, 1949
- LXXXIV. The flow of water in an inclined channel of rectangular sectionThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1925