A mathematical model is developed for the calculation of flow field and bed
topography in curved channels with an erodible bed. A small perturbation approach is used
to linearize the governing equations.
The downstream convective acceleration of the secondary flow is shown to give
rise to a phase lag between secondary flow and channel centerline curvature, and also to
suppress the magnitude of the secondary flow. The model further accounts for the
convective transport of primary flow momentum by the secondary flow. This oft-neglected
influence of the secondary flow is shown to be an important cause of the redistribution of
the primary flow velocity.
The governing equations retain the full coupling between the flow field, the bedload
transport, and the bed topography. This coupling is shown to increase significantly the
lateral bed slope in the upstream part of a channel bend, even beyond the value for fully
developed bend flow which is approached in the downstream part of a channel bend. This
coupling is also shown to give rise to resonant behavior for certain combinations of input
variables; the common origin of the two phenomena is explained. The predicted flow field
and bed topography compare very well with both laboratory and field data.
Further, assuming the banks to be erodible, the model is used to predict
wavelengths of river meanders. The results compare favorably with both laboratory and
Johannesson, Helgi; Parker, Gary.
Theory of River Meanders.
St. Anthony Falls Hydraulic Laboratory.
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