The method of Kalinin-Miljukov

Figure a: Hysteresis curve

The method of Kalinin-Miljukov states that the storm state in a flood wave is always unstationary. The results derived for the stationary state, applied for the unstationary (unsteady) storm is not fully correct, since in the case of unstationary flow, there is no unique volume/discharge relation.

Hysteresis curve (Figure a): storage versus outflow is not a single valued function.




Figure b: Characteristic length for Kalinin-Miljukov method

This method states that it is possible to define an unique function between discharge and volume if the channel is represented by a cascade of n linear reservoirs with the length L (characteristic length). The unsteady flow in those sections can be approximated by a quasi-stationary flow.

Figure b expresses that the discharges of the cross section r are assigned to the water levels in the cross section m, so that the discharges of the stationary discharge curve at the cross section m can be assigned to the corresponding unstationary ones at the cross section r.

A straight line is assumed for QAi associated with a volume Si, which corresponds to profile r. For unstationary flow the line is AB and for stationary flow CD. And the volumes over the areas AOC and ODB are represented, respectively.

In addition, h represents the water depth, Jw the water level downward gradient, Js the river bed gradient and Jsteady state the gradient of the straight lines at stationary conditions.

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Hydrological modelling






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