Analogy Between Surface Shock Waves in a Liquid and Shocks in Compressible Gases: Experimental Study of Hydraulic-Jump Interactions

Abstract

It has been known for some time that an analogy exists between the flow of a liquid with a free surface and the flow of a compressible gas. A less accurate analogy has been shown to obtain between hydraulic jumps and compression shocks. The interaction of shocks can occur in two forms; the regular or two-shock configuration and the Mach or three-shock configuration. The latter configuration is not yet completely understood, either in the case of hydraulic jumps in a free-surface liquid or in the case of shocks in a compressible gas. This experimental study was primarily concerned with the Mach interactions of hydraulic jumps. The conclusions of this study are: (a) there is a definite disagreement between experiment and existing theory; (b) a depth discontinuity, or wave, rather than a velocity discontinuity separates the region behind the Mach wave from the region behind the reflected wave; (c) there is evidence that, for interactions of weak hydraulic jumps, there is a deviation from constant depth between waves; (d) the Mach wave is convex for the interaction of the stronger hydraulic jumps, but is concave for the interaction of weak hydraulic jumps; (e) measurements should not be made so as to allow for curvature of the Mach without considering the curvature of the incident and reflected waves in the neighborhood of the triple point.