A.A.Riabenko Contemporary state and problems of undular jump theory |
Applied hydromechanics, Vol. 18 (90) ¹ 1, (2016) |
| The detailed analysis of current information about undular jump are given. The identified deficiencies, misconceptions and existing issues about this phenomenon are shown. The article identifies the differential equations, which are used to calculate the free-surface profile of undular jump. The positive and negative features of these equations and their solutions are given. The article gives the development of a principally original and new mathematical model for the wavelike near-critical flows including the undular jump. On the basis of this model, the author has derived and presents a combined differential equation with its general and specific solutions for the free-surface profile of the considered phenomena. The peculiarity of original mathematical model and its solutions is taking into account the possible hydrostatic and non-hydrostatic conditions specifically in the initial section of the undular jump and other types of the near-critical flows. Comparison of theoretical calculations with empirical data for a relevant range of conditions has provided a good convergence of the results and confirmed principal accurateness and applied value of the developed mathematical model. |
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KEY WORDS: cnoidal waves, near-critical flows, no hydrostatic pressure distribution, solitary wave, undular jump |
| TEXT LANGUAGE: Ukrainian |