Beyond Shallow Water: appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer Theory

Francesco de Vita (1) , Pierre-Yves Lagrée (2) , Sergio Chibbaro (3) , Stéphane Popinet (3)

1 Linné FLOW Center [Stockholm]
2 DALEMBERT - Institut Jean Le Rond d'Alembert
3 IJLRDA-FCIH - Fluides Complexes et Instabilités Hydrodynamiques

We study the flow of a thin layer of fluid over a flat surface. Commonly, the 1-D Shallow-water or Saint-Venant set of equations are used to compute the solution of such flows. These simplified equations may be obtained through the integration of the Navier-Stokes equations over the depth of the fluid, but their solution requires the introduction of constitutive relations based on strict hypothesis on the flow régime. Here, we present an approach based on a kind of boundary layer system with hydrostatic pressure. This relaxes the need for closure relations which are instead obtained as solutions of the computation. It is then demonstrated that the corresponding closures are very dependent on the type of flow considered, for example laminar viscous slumps or hydraulic jumps. This has important practical consequences as far as the applicability of standard closures is concerned.

Mots clés: Shallow Water; Saint-Venant; Boundary layer flows

Domaines: Mécanique des fluides [physics.class-ph]

Francesco de Vita, Pierre-Yves Lagrée, Sergio Chibbaro, Stéphane Popinet. Beyond Shallow Water: appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer Theory. European Journal of Mechanics - B/Fluids, 2019, 79, pp.233-246. ⟨10.1016/j.euromechflu.2019.09.010⟩. ⟨hal-02295398⟩