Citation

Gioia G, Chakraborty P, Gary SF, Zamalloa CZ, Keane RD. Proc. Natl. Acad. Sci. U. S. A. 2014; ePub(ePub): ePub.

Affiliation

Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801.

Copyright

(Copyright © 2014, National Academy of Sciences)

DOI

10.1073/pnas.1015183108

PMID

21444786

Abstract

Hydraulic jumps are a common feature of rivers and waterways, where they can be found close to spillways, weirs, rocky ledges, and boulders. People adrift upstream of a hydraulic jump are liable to become trapped in the turbulent roller of the hydraulic jump. For this reason, hydraulic jumps have been termed "drowning machines" and are recognized as a public hazard. We use experiments and theory to show that on average a buoyant object spends a time τ/p trapped in a jump, where τ is the period of a harmonic process inherent in the jump, and p is the probability that the object will escape in any time interval τ. The probability p is governed by the statistical theory of extreme values and depends primarily on the ratio between the density of the object and the density of the fluid. We use our results to draw conclusions that might prove to be useful to public-safety agencies intent on carrying out tests in drowning machines. Our results can also be used to predict the amount of flotsam that accumulates at the toe of a hydraulic jump.

Language: en