Journal of Fluid Mechanics



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An experimental investigation of the stability of the circular hydraulic jump


JOHN W. M. BUSH a1, JEFFREY M. ARISTOFF a1 and A. E. HOSOI a2
a1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
a2 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Article author query
bush jw   [Google Scholar] 
aristoff jm   [Google Scholar] 
hosoi ae   [Google Scholar] 
 

Abstract

We present the results of an experimental investigation of the striking flow structures that may arise when a vertical jet of fluid impinges on a thin fluid layer overlying a horizontal boundary. Ellegaard et al. (Nature, vol. 392, 1998, p. 767; Nonlinearity, vol. 12, 1999, p. 1) demonstrated that the axial symmetry of the circular hydraulic jump may be broken, resulting in steady polygonal jumps. In addition to these polygonal forms, our experiments reveal a new class of steady asymmetric jump forms that include structures resembling cat's eyes, three- and four-leaf clovers, bowties and butterflies. An extensive parameter study reveals the dependence of the jump structure on the governing dimensionless groups. The symmetry-breaking responsible for the asymmetric jumps is interpreted as resulting from a capillary instability of the circular jump. For all steady non-axisymmetric forms observed, the wavelength of instability of the jump is related to the surface tension, $\sigma$, fluid density $\rho$ and speed $U_v$ of the radial outflow at the jump through $\lambda\,{=}\,(74\pm7)\sigma/(\rho U_v^2)$.

(Received March 3 2003)
(Revised November 14 2005)



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