Mathematical and hydraulic modelling of undular jump

The article considers the problem of undular jump’s mathematical and hydraulic modelling. The cases of undular jump formation during different hydrotechnical constructions work are given. If the specifity of undular jump, especially wavelike free-surface and departure of from pressure distribution will not be taken into account, it can put to difference between designed and real hydraulic regimen. This factor can bring to miscalculation during designing, building and exploitation of constructers. All that shows the issue urgency of undular jump characteristics calculations and modelling. The article gives existent differential equations of free-surface of near-critical flows, which include undular jump.

The disadvantage of  given differential equations and their solutions are made, based on produced analysis. Consequently, addressing the mentioned existing misconceptions about the undular jump, it is necessary take into account inclination and curvature of streamlines in initial section of considered phenomena. The original mathematical model of near-critical flow, which takes into account this factor, are suggested. On the basis of this model, the differential equation was derived – with its general and specific solutions – for the free-surface profile of the considered phenomena.

The results of undular jump laboratory researches, which were made on experimental setup, are demonstrated. The comparison of theoretical calculations with experimental data has provided a good convergence of the results. 

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