The Hydraulic Jump in Terms of Dynamic Similarity

Abstract
Since Bidone's classical “Memoire”, the first to describe the hydraulic jump, this fascinating and puzzling phenomenon has been the subject of repeated experimental investigation. Most of the work has dealt with what may be termed the “vertical” elements of the jump, such as the relation between the lower and upper stages, the height of the standing wave, etc. Scarcely any data are available, at least in systematic form, with regard to what may be termed the “longitudinal elements”, such as the length of the jump, the profile of the surface of the roller, etc. The importance of such data is obvious. In designing stilling-basins at the toes of spillways, in laying out devices to prevent erosion below sluices, and in other similar cases, knowledge of the longitudinal elements is indispensable. During 1932-33 the longitudinal elements of the jump was the subject of systematic research in the Fluid Mechanics Laboratory of Columbia University, in New York, N. Y. A particular feature of the work was, that in interpreting and systematizing the results obtained, recourse was taken to the principle of dynamic similarity and the final data were presented in generalized dimensionless form. Dimensionless presentation in terms of dynamic similarity is known to have yielded splendid results and has become a matter of course when dealing with flow in closed conduits. On the other hand, its application to open flow, with the exception of models of rivers, has not been as widespread as could be expected. It also appears that the basic premises which should govern the approach to open-flow problems, are not always clearly understood and that at times investigators are prone to select parameters non-judiciously. An example is the frequent use of the so-called “Boussinesq number.” The experiments described herein were referred to a general dynamic characteristic, “the kinetic flow factor”. The results obtained seem to have confirmed the usefulness of the general methods applied and are claimed to have given the first comprehensive picture of the longitudinal features of the hydraulic jump in general.

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