The Role of Near-Bed Turbulence in the Inception of Particle Motion

by A.N. Papanicolaou

1. Introduction

The analysis of the turbulence properties of boundary layer flows has been a vibrant area of research for almost a century. Early pioneering work was directed towards the formulation of time and space averaged representation of flow characteristics, culminating in the now familiar boundary layer theory. Nowadays, the discovery of the so-called bursting phenomenon in turbulent flows by Kline et al. (1967)  (i.e., the cycle of sweeps (u>0, w<0), ejections (u<0, w>0), inward (u<0, w<0), and outward interactions (u>0, w>0), where, u is the fluctuating velocity component in the longitudinal direction and w is the fluctuating velocity component in the vertical direction) generated a new interest in further studying the structures of boundary layer turbulence and then applying this new knowledge to the initiation of spherical particles motion problem.

In an attempt to link the characteristics of turbulent episodes with the entrainment of sediment, several researchers (e.g., Keshavarzy and Ball, 1999; Kaftori et al., 1998; Nino and Garcia, 1996; Kirkbride, 1994; Lapointe, 1992; Rashidi et al. (1990); Dyer and Soulsby, 1988; Grass, 1983; Sumer and Deigaard, 1981; Cleaver and Yates, 1976) have considered that the sweeps cause the initiation of bedload motion in a stream bed, while the ejections (or, interchangeably, bursts) are primarily responsible for the particles' suspended motion. The reasoning behind this consideration is that the sweeps and ejections are the only events associated with the bursting process that contribute positively to the fluctuating Reynolds shear stress component (-uw) and, therefore, augment the turbulence production term.

Recently, a second school of thought (e.g., Nelson et al., 1995) has supported the opinion that the sweeps are not the only events responsible for bedload transport of gravel, but thatthe outward interactions are also responsible. Nelson et al., (1995) have clearly shown that when the magnitude of the outward interactions increases comparatively to the other events of a bursting cycle, the sediment flux increases too, although the magnitude of the Reynolds stress decreases. They found a poor correlation between the sediment flux and the Reynolds shear stress component (-uw). Instead, they have indicated a significant positive correlation between the streamwise instantaneous velocity U (where  and is the local time averaged velocity) and the sediment flux for flow conditions well above the sediment incipient motion conditions.

Along these lines, Sterk et al. (1998), Clifford et al. (1991), and Williams et al. (1989)  have suggested that the normal stresses in the longitudinal and vertical direction, u² and w², may be more important in sediment transport than the shear stress component (-uw). This suggests that calculations of sediment flux should not be based on shear stress alone, as many of the equations predicting bedload and/or suspension rates generally do. Moreover, it was shown that although the (-uw) term remains the principal shear stress component, its contributions to the total turbulent stress are much less than those of the u², w². For the stresses involving mixed products (e.g., ) (Clifford et al., 1991; Corrsin, 1967). According to Corrsin (1967), it is likely that the mixed terms might significantly contribute to the initiation of sediment motion.

These prior studies suggest that the linkage of the sediment motion with the turbulent flow components responsible for the initiation of motion remains an open case despite the substantial progress that has been attained in the sediment-flow interaction research over the last decade. It is questionable as to whether the statistical characteristics of the (-uw) term are of the greatest importance in the prediction of the beginning of sediment entrainment. Nonetheless, the majority of the aforementioned studies have focused on the interaction of turbulence with sediment motion for flow conditions well above the critical sediment motion conditions (Julien, 1995). To the best of the author's knowledge, in none of these laboratory and field studies were the different turbulent events at flow conditions near the inception of sediment motion.

The primary motivation of this study is to identify the flow events that are responsible for the commencement of sediment (spherical particles) motion under different bed configurations. This was accomplished by performing incipient motion tests in a water-recirculating flume for three well defined surface-packing density configurations that simulate the isolated, wake interference, and skimming flow regimes (i.e., the term surface-packing density denotes the inter-particle distance and is defined as the ratio between the projected plan area of all the particles to the total bed section within which the particles are located (Schlichting, 1979)). The instantaneous stress tensor in the vicinity of a particle was measured by using a 3-D Laser Doppler Velocimeter (LDV). The results were analyzed to determine the relative importance of the various stress components, as well as the contributions during the four quadrants of the turbulent bursting cycle.

Abstract

 1. Introduction

 Next Section: Experimental Facility

 3. Methodology-Results

 4. Conclusions

 Acknowledgements

 References