Structure of the hydraulic jump in convergent radial flows

Kseniya A Ivanova (1) , S. Gavrilyuk (1)

1 IUSTI - Institut universitaire des systèmes thermiques industriels

We are interested in modelling of multidimensional turbulent hydraulic jumps in convergent radial flow. To describe the formation of intensive eddies near the free surface (rollers) at the front of the hydraulic jump, a new model of shear shallow water flows is used. The governing equations form a non–conservative hyperbolic system with dissipation source terms. The structure of equations is reminiscent of generic Reynolds-averaged Euler equations for barotropic compressible turbulent flows. Two types of dissipative terms are studied. The first one corresponds to Chézy-like dissipation rate, and the second one to a standard energy dissipation rate commonly used in compressible turbulence. Both of them guarantee the positive definiteness of the Reynolds stress tensor. The equations are rewritten in polar coordinates and numerically solved by using an original splitting procedure. Numerical results for both types of dissipation are presented and qualitatively compared with the experimental works. The results show both experimentally observed phenomena (cusp formation at the front of the hydraulic jump) as well as new flow patterns (the shape of the hydraulic jump becomes a rotating square).

Mots clés: turbulent hydraulic jump; convergent radial flow; radial symmetry breaking; non- conservative hyperbolic equations

Domaines: Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique mathématique [math-ph]; Physique Numérique [physics.comp-ph]

Kseniya A Ivanova, S. Gavrilyuk. Structure of the hydraulic jump in convergent radial flows. Journal of Fluid Mechanics, 2019, 860 (pp. 441-464). ⟨hal-01795885⟩