The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

Abstract

This study demonstrates the importance of a sophisticated sub-grid model when performing a depth-averaged unsteady RANS simulation of a shallow flow. The reduction of resolution and the spatial dimensions exclude important physical processes as present in three-dimensional turbulence. Especially the effect of the bottom turbulence on the formation of horizontal eddies appears of key importance. A method is proposed to incorporate these effects by means of a kinematic simulation that mimics the residual turbulent fluctuations in a straight channel flow after depthaveraging. This method is developed in the context of the evolution of large eddies in a shallow mixing layer. A comparison with experiments shows that the proposed method works satisfactory. Naturally, it does not fully account for the omission of all 3D-effects.

Importance of frictional effects and jet instability on the morphodynamics of river mouth bars and levees

“…In a three‐dimensional LES model for shallow water problems, the mesh size should be chosen in such a way that the cutoff wave number (proportional to the inverse of the turbulent eddy length scale) lies in the inertial subrange [ van Prooijen , ]. Therefore, the horizontal resolution of a LES model should at least be of the order of the water depth, so that the large‐scale anisotropic turbulence is fully resolved [ van Prooijen and Uijttewaal , ]. This requirement still implies long computational times, because in order to resolve vortices with the length scale of the depth, the mesh size should then be at least an order of magnitude smaller than the water depth [ van Prooijen , ].…”

Low-order modelling of three-dimensional surface waves in liquid film flow on a rotating disk

“…The value of adopted in this study is significantly smaller than the values used in studies on shallow-water turbulence where is often greater than 50 (Hinterberger et al. 2007; van Prooijen & Ujittewaal 2009). This lower backscatter constant can be attributed to the presence of the free surface, which absorbs turbulent energy during wave propagation.…”

“…The use of high-fidelity direct numerical simulations makes it possible to formulate the energy balance that encompasses the backscattering effect in wavy film flows. Thus, more accurate backscatter models similar to those in shallow waters (van Prooijen & Ujittewaal 2009; Klöwer et al. 2018) can be established.…”

“…To address both scales, the velocity components are initially decomposed into filtered (resolved) and sub-grid scale (unresolved) components. This decomposition allows for the derivation of filtered versions of the depth-averaged equations, drawing inspiration from the literature on depth-averaged large-eddy simulations (DA LES) for turbulent shallow waters (Hinterberger et al 2007;van Prooijen & Ujittewaal 2009). In these simulations, the grid size is typically comparable to the water depth, leading to the term sub-depth scale instead of sub-grid scale.…”

“…The use of high-fidelity direct numerical simulations makes it possible to formulate the energy balance that encompasses the backscattering effect in wavy film flows. Thus, more accurate backscatter models similar to those in shallow waters (van Prooijen & Ujittewaal 2009;Klöwer et al 2018) can be established. In addition, a more sophisticated experimental set-up capable of directly acquiring real-time film thickness data, instead of measuring the displacement of the liquid-gas interface, should be implemented.…”