7052

• UCREFRP Catalog Number: 7052
• Author: Andrews, E. D. and J. M. Nelson
• Title: Topographic Response of a Bar in the Green River, Utah to Variation in Discharge
• USFW Year: 1989
• USFW - Doc Type: American Geophysical Union
• Copyright Material: YES

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Andrews and Nelson

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Finally, the interrelation of these three elements and their combination into a
topographic evolution model is briefly discussed.

The Flow Model

The fundamental requirement of a coupled flow-bed topography model is a
careful treatment of the fluid dynamics. In particular, the response of the flow to
topographic non uniformity must be treated accurately, because the forcing on the
flow field due to the nonuniformity of the bed has a significant influence upon the
topography. It has been demonstrated [Yen and Yen, 1971; Dietrich and Smith,
1983; Berg and Odgaard, 1988] that the convective accelerations due to planform
and topographic nonuniformity in channels are often of the same order of magnitude
as the pressure gradient and stress divergence in the local momentum balance.
Thus, a model that is based upon a perturbation expansion a.bout a. zero-order
steady uniform flow will not provide a satisfactory simulation of conditions in a
reach with complex topography. Accordingly, the non-linear treatment originally
developed by Smith and McLean [1984] and subsequently expanded upon and
applied to the mobile bed by Nelson and Smith [1989a., b, this volume] is employed
here. The mathematical development of this treatment is presented in detail in the
above work, and will not be repeated here. In order to interpret the results of the
evolution model presented below, however, it is useful to briefly restate the basic
assumptions used in developing the flow model. They are as follows:

The flow is treated as quasi-ilteady.
The pressure distribution is assumed to be hydrostatic.
Lateral stresses and boundary layers are neglected.
The vertical velocity and length scales are an order of magnitude smaller
than the crosS-iltream velocity and length scales which are, in turn, an order
of magnitude smaller than the streamwise velocity and length scales.
The vertical structure of the zero-order streamwise velocity field is given by
a similarity structure (e.g., a logarithmic or quasi-logarithmic profile). One
of the consequences of this assumption is that, at lowest order, the
boundary shear stress is related to the vertically-averaged velocity field by
a drag coefficient (Note that this coefficient depends upon local roughness
and is not necessarily spatially constant).
Cross-iltream secondary flows associated with both channel planform and
streamline curvature are evaluated.
Advection of streamwise and crOSS-iltream momentum fluxes by the
secondary flows are neglected [although they may be included iteratively,
see Nelson and Smith, 1988b].

The inputs required for this computational model are the planform and
topography of the channel, the local roughness lengths in the channel, and the
discharge. The flow model computes three-dimensional velocity fields; downstream
and cl'OSS-6tream boundary shear stresses, and water-ilurface elevation in the
channel. The predicted values can be expected to reproduce the actual values with
reasonable accuracy, provided that none of the assumptions above are violated. In
practice, the assumptions restrict the application of this model to channels where
depths are substantially smaller than widths and streamwise variations in width and
topography are gentle. Thus, the model is not valid for the case of rapid width
variations (i.e., banks at angles greater than twenty or thirty degrees to the
downchannel direction), and cannot be expected to give good results if largEHlcale
bed slopes along the direction of fluid motion exceed ten d~ees or so. These
situations, however, are relatively uncommon, especially in allUVial channels.

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