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The U.S. Army Corps of Engineers HEC-RAS model (Version 4.0) can perform three functions: (1) steady flow, (2) unsteady flow, and (3) movable boundary flow.
The steady flow component uses the standard step method for the solution of (the equation of) steady gradually varied flow.1
The unsteady flow component uses a numerical solution of the equations (of water continuity and motion)
governing gradually varied unsteady
flow in open channels. The movable boundary component uses the sediment continuity and (one of) several
sediment transport equations to calculate
river bed aggradation/degradation.
• When should unsteady flow be used?
This question is of considerable practical
interest, since unsteady flow is significantly more complex and requires more data than steady flow.
However, the answer is not straightforward, and requires some elaboration.
• Steady vs unsteady flow
Under steady flow, the user inputs as boundary conditions a discharge upstream and a stage downstream.
The model calculates stages throughout the interior points, keeping the discharge constant.
Under unsteady flow, the user inputs a discharge hydrograph at the upstream boundary and a discharge-stage rating
at the downstream boundary. The model calculates discharges and stages throughout the interior points.
Under steady flow the discharge-stage ratings are unique, i.e., kinematic. On the other hand, under unsteady flow the model itself calculates (dynamic)
looped discharge-stage
ratings according to the variabilities of the flow. Therefore, the specification of a unique discharge-stage rating at the downstream boundary
contradicts the solution at that boundary.2 The model cannot be kinematic at the downstream
boundary and dynamic everywhere else!
A way out of this difficulty is: (1) to move the downstream boundary further downstream, (2) to specify the unique discharge-stage rating at the
artificial downstream boundary, and (3) to let the model itself calculate the looped ratings at the interior points,
including the point where the real downstream boundary is located.3 Despite its
apparent artificiality, this procedure works well
and circumvents the need to know the discharge-stage rating (at the downstream boundary) before it is calculated.
• Kinematic vs dynamic waves
The decision to use unsteady flow will depend on whether the wave to be modeled is kinematic
or dynamic. If the wave is kinematic, (1) the discharge will not vary in space;
(2) the discharge-stage ratings will be unique; and (3) the downstream boundary can be specified as unique.
In this case, the solutions of steady and unsteady flow are essentially the same; therefore, the unsteady flow calculation is not needed.
On the other hand, if the wave is dynamic, (1) the discharge will vary in space, attenuating as it moves downstream;
(2) the calculated discharge-stage ratings
will not be unique; and (3) for better accuracy, the downstream boundary should be artificially moved downstream to allow for an unsteady looped rating to develop
at the real downstream boundary. In this case, the unsteady flow calculation is justified, assuming of course, that the wave is truly dynamic.
• Use of unsteady flow in channel design
This situation begs the question of whether a certain flood wave can be construed as either kinematic or dynamic.
Or, better yet, whether a dynamic wave should be used at all to determine stages in the design of channel improvement projects.
On typical projects, of limited channel lengths, a kinematic wave, which keeps its discharge constant,
is a better assumption than a dynamic wave, which attenuates its discharge. Indeed, the kinematic wave assumption assures that the
channel will contain all waves, kinematic or dynamic. Viewed in this light, the use of a dynamic wave for the calculation of stages in the
design of channel improvements projects does not appear to be warranted.
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