The role of gravity and viscous forces in the formation of the circular hydraulic jump

Roger Khayat (Western University)

Time:

2PM Wednesday, 22 April 2026

Location:

Science East, E0.32

We examine the structure of the continuous circular hydraulic jump and recirculation for a jet impinging on a disk (see figure below). We use a composite mean-field thin-film approach consisting of subdividing the flow domain into three regions of increasing gravity strength: a developing boundary layer near impact, an intermediate supercritical viscous layer, and a region comprising the jump and subcritical flow. Unlike existing models, the approach does not require any empirically or numerically adjusted boundary conditions. We demonstrate that the stress or corner singularity for a film draining at the edge is equivalent to an infinite slope of the film surface, which we impose as the downstream boundary condition. The model is validated against existing experiment and numerical simulation of the boundary-layer and Navier-Stokes equations. We find the flow in the supercritical region (upstream of the jump) remains insensitive to the change in gravity level and disk size but is greatly affected by viscosity. We also show that the existence of the jump is not necessarily accompanied by recirculation which is strongly dependent on the upstream curvature and steepness of the jump. Finally, our calculations suggest that the surface separating the regions of existence/non-existence of the recirculation is given by the universal relation Re^10/3Fr²=9r_∞⁹/50 in the parametric space, where Re and Fr are the Reynolds and Froude numbers based on the impinging jet velocity and radius, and is the disk radius in units of the jet radius. Various flow configurations will be discussed (see references below).

References

W. Wang, A. Baayoun & R. E. Khayat. The characteristics of the circular hydraulic jump and vortex structure. J. Fluid Mech. (2024) 980, A15.

W. Wang, A. Baayoun & R. E. Khayat. A coherent composite approach for the continuous circular hydraulic jump and the vortex structure. J. Fluid Mech. (2023) 966, A15.

A. Baayoun & R. E. Khayat. Transient spread of a circular liquid jet and hydraulic jump formation. J. Fluid Mech. (2022) 947, A34.

Yunpeng Wang & Roger E. Khayat. The effects of gravity and surface tension on the circular hydraulic jump for low and high-viscosity liquids: A numerical investigation. Phys. Fluids (2021) 33, 012105 1-10.

Y. Wang & R. E. Khayat. The influence of heating on liquid jet spreading and hydraulic jump. J. Fluid Mech. (2020) 883, A59 1-37.

Y. Wang & R. E. Khayat. The role of gravity in the prediction of the circular hydraulic jump radius for high-viscosity liquids. J. Fluid Mech. 862 (2019) 128-161.

Yunpeng Wang & Roger E. Khayat. Impinging jet flow and hydraulic jump on a rotating disk. J. Fluid Mech. 839 (2018) 525-560.

R. E. Khayat. Impinging planar jet flow and hydraulic jump on a horizontal surface with slip length. J. Fluid Mech. 808 (2016) 258-289.

Jiangang Zhao and Roger E. Khayat. Spread of non-Newtonian liquid jet over a horizontal plate. J. Fluid Mech. 613 (2008) 411-443.