The influence of surface tension on the circular hydraulic jump

Abstract

We present the results of a combined theoretical and experimental investigation of the influence of surface tension σ on the laminar circular hydraulic jump. An expression is deduced for the magnitude of the radial curvature force per unit length along a circular jump, F c = −σ (s − R)/R j , where R j is the jump radius, and s and R are, respectively, the arclength along the jump surface and radial distance between the nearest points at the nose and tail of the jump at which the surface is horizontal. This curvature force is dynamically significant when 2σ/(ρgR j H) becomes appreciable, where H is the jump height, ρ the fluid density and g the acceleration due to gravity. The theory of viscous hydraulic jumps (Watson 1964) is extended through inclusion of the curvature force, and yields a new prediction for the radius of circular hydraulic jumps. Our experimental investigation demonstrates that the surface tension correction is generally small in laboratory settings, but appreciable for jumps of small radius and height.

Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole

“…The first modern description of this phenomenon dates back to Lord Rayleigh [1], who developed a momentum-balance theory to describe it, but did not take viscosity into account. The standard theory for viscous fluids is due to Watson [2], and has been further improved through the inclusion of surface tension by Bush and Aristoff [3]. The circular jump is an intricate phenomenon of fluid dynamics: while it suffices to open a kitchen tap to observe it, the theory describing it becomes tremendously complicated for all except its most simple applications.…”

Simulation results and applications of an advection bounded scheme to practical flows

“…of Brechet and Néda [30], and r jump = Q possesses its maximum (see [32]). The 2.5D version of the Freeflow code [20] equipped with the TOPUS scheme was run on this problem using three meshes, namely 200 × 126 (δ x = δ y = 0.00025 m); 400 × 252 (δ x = δ y = 0.000125 m) and 800 × 504 (δ x = δ y = 0.000625 m) computational cells (known hereafter as Mesh I, Mesh II and Mesh III, respectively).…”

A constrained variational model for radial symmetry breaking

“…Aristoff, Bush, Hosoi and coworkers [3,1,4,5] performed careful and thorough experiments, and interpreted the phenomenon of non-circular jumps to be due to surface tension. A model including the capillary effect was proposed and studied by Martens et al [11].…”