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101
IWA Publishing 2004
Journal of Hydroinformatics
06.2
2004
Lateral structure of uniform flow
Robert J. Sobey
ABSTRACT
The concept of uniform flow is traditionally associated with a cross-section-integrated description of
Rodney J. Sobey
Department of Civil and Environmental
channel flow. In some analyses of flow in wide channels, it may be appropriate to adopt a
Engineering,
Imperial College London,
depth-integrated description. The ensuing lateral structure of the depth-integrated flow is
London SW7 2AZ,
UK
investigated at uniform flow. The steady state ordinary differential equation for the lateral structure
E-mail: r.j.sobey@imperial.ac.uk
is established, along with the formulation as a boundary value problem. An integral part of the
formulation is the relationship between the channel resistance models for cross-section-integrated
and depth-integrated descriptions, respectively. Predictions are shown for a rectangular channel and
for an irregular channel.
| uniform flow, natural channels, lateral profile, eddy viscosity
Key words
INTRODUCTION
mass and momentum fluxes in both the longitudinal and
Uniform flow in a channel is a flow state that is rarely
lateral directions. The vector momentum equations must
experienced but it is nonetheless influential in character-
also include lateral momentum transfer, without which
izing channel flows. In particular, it has a fundamental
there would be slip at lateral boundaries and no lateral
role in characterizing channel friction. The familiar chan-
boundary layer structure. Channel resistance is here
nel resistance closure models, Chezy, DarcyWeisbach
`
characterized by a bottom friction factor (C or f or n) to
and Manning, are uniform flow formulae. In steady
represent shear in the vertical and an eddy viscosity e to
gradually varied flow, uniform flow is the asymptotic state.
represent shear in the horizontal. Together, the bottom
In unsteady flow, steady gradually varied flow is the local
friction factor and the horizontal eddy viscosity assume
time-averaged flow.
the role of the cross-section-averaged friction factor in the
The traditional analysis of uniform flow is based on a
cross-section-integrated description.
cross-section-integrated description of channel flow. The
A depth-integrated description provides the oppor-
flow is characterized by the cross-section-integrated flow
tunity to predict the lateral flow structure at uniform flow.
As context, this paper will initially review the traditional
is characterized by a constant cross-section-averaged
cross-section-integrated prediction of uniform flow con-
friction factor, C, f or n, depending on the closure
ditions in a natural channel. It will then consider the
model. At uniform flow, Q, the flow cross-section A
definition of uniform flow conditions with a depth-
and the water surface slope ∂h/∂x are all constant.
integrated description of channel flow. An ordinary differ-
There is no prediction of flow structure within the cross
ential equation is established to describe the lateral flow
section.
structure qx(y) at uniform flow. The associated boundary
A depth-integrated description of channel flow pro-
value problem is formulated, and solved numerically. An
vides some flow structure. The flow is characterized by
depth-integrated flows qx in the longitudinal direction and
integral part of the analysis is the relationship between the
qy in the lateral direction, together with the water surface
cross-section-integrated friction factor and the combi-
elevation h. The conservation equations must now include
nation of bottom friction factor and horizontal eddy
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