An experimental investigation of turbulent free-surface flows over a steep permeable bed

Abstract

Steep streams involve shallow, supercritical turbulent flows over a permeable bed made up of coarse particles. They usually exhibit higher flow resistance and stronger mass and momentum exchanges between the stream and subsurface flow than low-gradient streams. Describing their flow dynamics using generalised Manning–Strickler equations has led to empirical relationships with weak predictive power (errors between predictions and data of over one order of magnitude). We studied shallow turbulent flows by employing a mesoscopic approach based on the double-averaged Navier–Stokes equations. More specifically, we were concerned with the possibility of modelling the turbulent and dispersive shear stress equations using simple algebraic equations. To that end, we studied shallow, supercritical turbulent flows over a sloping bed made up of randomly packed spherical particles. Using visualisation techniques based on particle velocimetry imaging and refractive index matched scanning, we were able to reconstruct the velocity field throughout the bed and stream, far from the sidewalls, and estimate the contributions of the dispersive and turbulent shear stresses to the total shear stress. The dispersive shear stress represented less than 20 % of the turbulent shear stress, but because it was concentrated within a thin layer (called the roughness layer) where it outweighed the turbulent shear stress, it had a significant influence on the mean velocity profile. We proposed an algebraic closure equation for dispersive shear stress, based on the mixing-length model used for turbulent shear stress, and we found that it captured closely the mean-velocity and turbulence-intensity profiles of shallow flows over horizontal or sloping permeable beds. Our data suggest that flow dynamics was affected largely by turbulence damping, drag forces and dispersion within the roughness layer, which may explain why steep streams differ from low-gradient streams.

Fluid‐Driven Transport of Round Sediment Particles: From Discrete Simulations to Continuum Modeling

“…On one hand, we use the hydraulic radius to estimate the bed shear stress which tends to underestimate the value (J. Guo, 2015). On the other hand, a similar low threshold for sediment transport is also observed in a related experimental setup (Heyman et al., 2016) and it has been shown to not be a result of the sidewall influence on turbulence (Rousseau & Ancey, n.d). Also as seen in the movies (Movies S1–S5) of the simulations, the behavior of the particles at the lowest τ * values seems to correspond to the Intermittent Bulk Transport regime (Pähtz & Durán, 2018a) in which τ * is above the rebound threshold but below the impact entrainment threshold, and the transported particles rebound for a relatively long period on the bed surface before depositing.…”

Using Different Classic Turbulence Closure Models to Assess Salt and Temperature Modelling in a Lagunar System: A Sensitivity Study

“…Typical summer salinity values, as in June 2001, were in the range of (30-34) PSU (which are values close to the ocean salinity), whereas low values (<5 PSU) were found close to the major river boundaries (stations 3, and 4) or at the far end areas (stations 6, 7 and 8) (30-33) PSU. The water temperature was in the range of (13)(14)(15)(16)(17)(18) • C for spring and (18-24) • C for summer, typical values for those seasons. The model used in this work is the baseline Mike3-HD [50,61], which is based on the numerical solution of the two/three-dimensional incompressible Reynolds-averaged Navier-Stokes equations, subject to the assumptions of Boussinesq and of hydrostatic pressure and consists in a system of continuity, momentum, temperature, and salinity equations.…”

“…The most basic assumption constitutes the so-called mixing length of the Prandtl model [14], which assumes that the fluid flow conserves its macroscopic properties for a characteristic length scale of the flow before mixing with the surrounding fluid. For instance, Rousseau and Ancey [15] managed to capture the mean-velocity and 2 of 25 turbulence-intensity profiles of shallow flows over a horizontal or sloping permeable bed by using an algebraic closure equation for dispersive shear stress based on the mixinglength model. Nevertheless, in most complex flows, this type of formulation falls short of capturing the complexity of the turbulence.…”

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

“…2017; Kim et al. 2020; Rousseau & Ancey 2022). Bed permeability was found to increase friction coefficient, reduce the wall-blocking effect due to impermeable rough walls, and reduce near-bed anisotropy in turbulence intensities.…”

“…Few experimental studies have evaluated turbulence characteristics over flat permeable beds (Zagni & Smith 1976;Zippe & Graf 1983;Manes et al 2009;Suga et al 2010;Manes, Poggi & Ridolfi 2011;Voermans et al 2017;Kim et al 2020;Rousseau & Ancey 2022). Bed permeability was found to increase friction coefficient, reduce the wall-blocking effect due to impermeable rough walls, and reduce near-bed anisotropy in turbulence intensities.…”