River-Meander Model: I. Development

Meander flow and meander‐planform development are described. The basis is a steady, two‐dimensional model of flow and bed topography in an alluvial channel with variable curvature. The model is developed from the equations for conservation of mass (water and sediment) and momentum, and from a stability criterion for sediment particles on the stream bed. By order of magnitude considerations and linearization, these equations are reduced to those of a damped, oscillating system. The meander development is described by forcing a traveling, small‐amplitude channel alignment wave on the system, and determining the growth characteristics of the wave. The growth rate of the amplitude is determined by relating the alignment wave and the change in channel alignment through a bankerosion model. Formulas are thereby developed for calculation of: (1) Velocity and depth distribution in meandering channels; and (2) rate and direction of channel migration. Laboratory and field data are used to verify the formulas.

[1]  Masanori Michiue,et al.  STUDY ON HYDRAULIC RESISTANCE AND BED-LOAD TRANSPORT RATE IN ALLUVIAL STREAMS , 1972 .

[2]  E. J. Hickin,et al.  The Character of Channel Migration on the Beatton River, Northeast British Columbia, Canada , 1975 .

[3]  Syunsuke Ikeda,et al.  Bed Topography in Bends of Sand‐Silt Rivers , 1985 .

[4]  A. Jacob Odgaard,et al.  Streambank erosion along two rivers in Iowa , 1987 .

[5]  A. Odgaard.  Meander Flow Model. II: Applications , 1986 .

[6]  H. D. Vriend,et al.  Bed deformation in curved alluvial channels , 1985 .

[7]  A. Jacob Odgaard,et al.  River‐Meander Model. II: Applications , 1989 .

[8]  A. Jacob Odgaard,et al.  Flow and Bed Topography in Alluvial Channel Bend , 1984 .

[9]  E. J. Hickin,et al.  Channel Migration and Incision on the Beatton River , 1983 .

[10]  W. Dietrich,et al.  Influence of the point bar on flow through curved channels , 1983 .

[11]  J. Hooke.  Magnitude and distribution of rates of river bank erosion , 1980 .

[12]  John F. Kennedy,et al.  TRANSVERSE BED SLOPES IN CURVED ALLUVIAL STREAMS , 1978 .

[13]  P. Blondeaux,et al.  A unified bar–bend theory of river meanders , 1985, Journal of Fluid Mechanics.

[14]  G. Parker,et al.  Bend theory of river meanders. Part 1. Linear development , 1981, Journal of Fluid Mechanics.

[15]  A. Jacob Odgaard,et al.  Flow processes in a curved alluvial channel , 1988 .

[16]  P. Kitanidis,et al.  Secondary current and river-meander formation , 1984, Journal of Fluid Mechanics.

[17]  Howard H. Chang.  Analysis of River Meanders , 1984 .

[18]  A. Jacob Odgaard,et al.  MEANDER FLOW MODEL. I: DEVELOPMENT , 1986 .

[19]  E. D. Andrews,et al.  Sorting of Bed Load Sediment by Flow in Meander Bends , 1985 .

[20]  E. J. Hickin.  The development of meanders in natural river-channels , 1974 .

[21]  L. B. Leopold,et al.  River channel patterns: Braided, meandering, and straight , 1957 .

[22]  John F. Kennedy,et al.  Flow in alluvial-river curves , 1983 .