An experimental investigation of the stability of the circular hydraulic jump

• Published in: Journal of fluid mechanics Vol. 558; pp. 33 - 52
• Main Authors: BUSH, JOHN W. M., ARISTOFF, JEFFREY M., HOSOI, A. E.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2006
• Subjects: Applied fluid mechanics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydraulic jump; Hydrodynamics, hydraulics, hydrostatics; Physics; Surface tension; Thin films; Vertical jet; Capillarity; Hydrodynamic instability; Instrumentation; Hydrodynamics; Interactions; Liquid layer; Experimental study; Hydraulic jump; Symmetry breaking
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112006009839

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 $\lambda\,{=}\,(74\pm7)\sigma/(\rho U_v^2)$.