The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds

Abstract

The purpose of the present paper is to provide further insights on the definition of the parameters of the log-law in open-channel flows with rough mobile granular beds. Emphasis is placed in the study of flows over cohesionless granular beds composed of monosized spherical particles in simple lattice arrangements. Potentially influencing factors such as grain size distribution, grain shape and density or cohesion are not addressed in this study. This allows for a preliminary discussion of the amount of complexity needed to obtain the log-law features observed in more realistic open-channel flows. Data collection included instantaneous streamwise and bed-normal flow velocities, acquired with a two-dimensional and two-component (2D2C) Particle Image Velocimetry (PIV) system. The issue of the non uniqueness of the definition of the parameters of the log-law is addressed by testing several hypotheses. In what concerns the von Kármán parameter, κ , it is considered as flow-independent or flow-dependent (a fitting parameter). As for the geometric roughness scale, k s , it results from a best fit procedure or is computed from a roughness function. In the latter case, the parameter B is imposed as 8.5 or is calculated from the best fit estimate. The analysis of the results reveals that a flow dependent von Kármán parameter, lower than the constant κ = 0.40 , should be preferred. Forcing κ = 0.40 leads to non-physical values of k s and would imply extending the inner layer up about 50% of the flow depth which is physically difficult to explain. Considering a flow dependent von Kármán parameter allows for coherent explanations for the values of the remaining parameters (the geometric roughness scale k s , the displacement height Δ , the roughness height z 0 ). In particular, for the same transport rate, the roughness height obtained in a natural sediment bed is much greater than in the case of bed made of monosized glass spheres, underlining the influence of the bed surface complexity (texture and self-organized bed forms, in the water-worked cases) on the definition of the log-law parameters.

Bursting phenomenon created by bridge piers group in open channel flow

“…There is a huge research interest among literature in the field of hydrodynamics around the flow obstruction [5,8,16,22,23,25,26,29,45,49]. Most researches have been conducted on the turbulent characteristics of flow over smooth and rough boundaries around single pier or obstruction [2,35,46,47], and fewer studies have been conducted on coherent flow structures to study the burst cycle dynamics and to understand the burst cycles correlation to flow [7,18,24,34].…”

Bursting phenomenon created by bridge piers group in open channel flow

“…There is a huge research interest among literature in the field of hydrodynamics around the flow obstruction (Karami et al 2014, Shrestha 2015, Beheshti and Ataie-Ashtiani 2016, Chavan et al 2019, Jalal and Hassan 2020, Li et al 2020, Gautam et al 2021, Yücesan et al 2021). Most researches have been conducted on the turbulent characteristics of flow over smooth and rough boundaries around single pier or obstruction (Nezu and Rodi 1986, Antico et al 2019, Vijayasree et al 2019, and fewer studies have been conducted on coherent flow structures to study the burst cycle dynamics and to understand the burst cycles correlation in flow (Nelson et al 1995, Cellino and Lemmin 2004, Keshavarzi et al 2014, Hanmaiahgari et al 2017. Kline et al (1967) first used the idea of a burst cycles for particle movement between turbulence and laminar zones near wall-boundary.…”

Water-Worked Bedload: Hydrodynamics and Mass Transport

“…Both studies are important from the perspective of designing river protection structures. One paper, by Antico et al [21], is dedicated to the velocity law in hydraulically rough flow over mobile granular beds, which falls into the third category. The fourth category presents important field studies by Radecki-Pawlik et al [22] on the Mlynne and Lososina streams in the Polish Carpathians; Huang et al [23] on the Three Gorges Reservoir (TGR) in China; and Przyborowski et al [24] on the Jeziorka River and Swider River in Poland.…”