AULOS software models interconnected open and closed channels

When do we need a supercritical flow solution?

The textbook analysis of the direction of flow control in steady flow makes life  unnecessarily complicated for modellers, as it assumes the solutions along the forward and backward dynamic wave characteristic are of equal importance. In practice the forward (downstream) characteristic is always dominant, as this takes the same direction as the kinematic wave characteristic, which determines the flow response to resistance effects.

The change from supercritical to subcritical flow merely changes the direction of the weak backward characteristic from downstream to upstream, which makes no difference in the usual case where flow is governed by the bed slope and resistance.

In model applications, the problem should not be seen as the selection of a supercritical or subcritical flow regime, but rather the selection of optimum locations for the upstream and downstream boundary of the study reach. Both should be sited where a good record of levels is available (or even better, a good level recorder should already have been sited at reach boundaries where the stream bed is naturally stable or fixed by an artificial structure).

Once the upstream and downstream boundaries are established, both should be specified as levels if that is what has been measured, and a correctly written solution code should solve the flow problem regardless of flow regime. If, rather than being estimated from a rating curve, the flow is continuously being measured directly (for example, through a turbine) then flow may also be used as an upstream boundary condition.

However a downstream flow boundary should be avoided, as this works against the dominant forward and kinematic wave characteristics which already govern the flow from upstream in both subcritical and supercritical flow, causing incompatibility which will usually crash the solution. Obviously this applies especially if an upstream flow boundary is given, as even if the boundary flows are identical the water mass within the reach will be fixed by some (arbitrary) initial calculation level rather than by the desired steady flow profile.

Testing on a model reach of alternating subcritical and supercritical flow is instructive in exploring the response of a package such as HEC-RAS in practice, and a verified test model is presented in Exercise QA6 "Mixed sub- and super-critical profile analysis" in the manual provided with the AULOS download.

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