Department of Civil & Infrastructure Engineering

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This study examines the probability for sediment entrainment to bed load and the probability for the threshold condition of sediment to be in suspension. The theoretical analysis is based on a simple one-sided exponential distribution of probability function. The probability distributions are derived from a truncated universal Gram-Charlier series expansion based on the exponential or Laplace-type distributions for turbulent velocity fluctuations. The key criterion of sediment entrainment is the hydrodynamic lift acting on a solitary particle to exceed submerged weight of the particle. In this way, a simple probability function for sediment entrainment to bed load in terms of Shields parameter containing the lift coefficient is obtained. It was found that the value of lift coefficient as 0.15 satisfactorily fitted the probability function versus Shields parameter curve with the experimental data. On the other hand, the key criterion of the threshold of sediment suspension is the fluctuations of the vertical velocity component to exceed terminal fall velocity of the particle. The probability function for the threshold of a sediment particle to be in suspension is obtained in terms of Shields parameter as a function of shear Reynolds number. Curves for different values of probabilities are drawn in respect to a Shields diagram. For the value of probability 0.05, the threshold of sediment suspension is indicated. The prediction curves for the threshold of sediment suspension are proposed in terms of Rouse number versus Shields parameter and also Shields parameter versus shear Reynolds number. © 2013 American Society of Civil Engineers.

World University root node

Journal of Hydraulic Engineering

Sediment entrainment probability and threshold of sediment suspension: Exponential-based approach

Water research

Aggregation and deposition kinetics of carboxymethyl cellulose-modified zero-valent iron nanoparticles in porous media

This study focuses on the double-averaged (DA) turbulence characteristics and the local flow characterization in the flow zones over and within the flow-gravel-bed interface. The cumulative running averaged (CRA) value of a turbulence quantity for a given interval (in this study, half of the gravel size) of flow measurement is the prerequisite to determine a complete DA value of that quantity. The CRA turbulence quantities within the interfacial sublayer require a longer distance to become spatially independent. A method is proposed to fit the log law for the DAvelocity over the bed and a polynomial law within the interfacial sublayer. The form-induced shear stress is 40% of the DA Reynolds shear stress occurring at the virtual bed level. The spatial velocity fluctuations diminish more rapidly than the temporal velocity fluctuations below the virtual bed level. In the inertial subrange of turbulent kinetic energy (TKE), the eddy size decreases significantly near the virtual bed level, and in the dissipation range, it increases slightly. The TKE fluxes directed downward and downstream compose the sweep events that are the prevailing mechanism within the interfacial sublayer. It is also confirmed by the quadrant analysis done for the bursting events. The form-induced energy fluxes below the crest level are comparable with the TKE fluxes. In the TKE budget, the forminduced diffusion rate is significant within the interfacial sublayer. The quantities constituting the TKE budget attain their peaks above the virtual bed level and reduce sharply below it. However, the pressure energy diffusion rate induces suction near the crest. The local flow characterization is done by separating the local velocity profiles into log, S-shaped, and accelerated classes. Unlike the velocity profiles per class, the profiles of turbulence quantities per class are almost indistinguishable within the interfacial sublayer. A comparison of the results of this study with those of previous studies shows more dissimilarities than similarities. © 2012 American Society of Civil Engineers.

Gravel-bed hydrodynamics: Double-averaging approach

An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady-state flow equation. It is established that the undular hydraulic jump phenomenon takes place because of the instability of the flow and can be described by the instability principle. The threshold of an undular hydraulic jump can be represented by a monotonic increasing curve of approaching flow Froude number versus boundary inclination. The elevation of the undular free surface increases with an increase in boundary inclination, but the amplitude of the free surface waves decreases with downstream distance. The theoretical results are well comparable with the experimental data. © 2012 American Society of Civil Engineers.

Free surface profiles of undular hydraulic jumps

Is the von Krmn constant affected by sediment suspension? The presence of suspended sediment in channels and fluvial streams has been known for decades to affect turbulence transfer mechanism in sediment-laden flows, and, therefore, the transport and fate of sediments that determine the bathymetry of natural water courses. This study explores the density stratification effects on the turbulent velocity profile and its impact on the transport of sediment. There is as yet no consensus in the scientific community on the effect of sediment suspension on the von Krmn parameter, . Two different theories based on the empirical log-wake velocity profile are currently under debate: One supports a universal value of =0.41 and a strength of the wake, , that is affected by suspended sediment. The other suggests that both and could vary with suspended sediment. These different theories result in a conceptual problem regarding the effect of suspended sediment on , which has divided the research area. In this study, a new mixing length theory is proposed to describe theoretically the turbulent velocity profile. The analytical approach provides added insight defining as a turbulent parameter which varies with the distance to the bed in sediment-laden flows. The theory is compared with previous experimental data and simulations using a k-turbulence closure to the Reynolds averaged Navier Stokes equations model. The mixing length model indicates that the two contradictory theories incorporate the stratified flow effect into a different component of the log-wake law. The results of this work show that the log-wake fit with a reduced is the physically coherent approximation. © 2012. American Geophysical Union. All Rights Reserved.

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Journal of Geophysical Research: Earth Surface

Is the von Kármán constant affected by sediment suspension?

This study is devoted to quantify the near-bed turbulence parameters in mobile-bed flows with bed-load transport. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. In the logarithmic law, the von Kármán coefficient decreases in presence of bed-load transport. The turbulent kinetic energy budget reveals that for the bed-load transport, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis, sweep events in mobile-bed flows are the principal mechanism of bed-load transport. The universal probability density functions for turbulence parameters given by Bose and Dey have been successfully applied in mobile-bed flows. © 2012 Versita Warsaw and Springer-Verlag Wien.

Acta Geophysica

Turbulence in mobile-bed streams

A theory of turbulent shear flow over a sand bed is developed, addressing the instability principle of the fluid-granular bed interface leading to the formation of ripples. The Reynolds-averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation are analyzed using a 1/7-power law of the time-averaged streamwise velocity and treating the curvilinear streamlines by the Boussinesq approximation. The integration of the RANS equations leads to a governing dynamical equation of flow over a mobile bed. A near-bed flow layer of 3.5 times the ripple height is considered being affected by the ripples. The dynamical equation of the mobile sand bed is based on the Exner's sediment continuity equation in conjunction with the Meyer-Peter and Müller bed-load transport formula as modified to account for the effect of local bed slope attributable to bed forms. The coupled dynamical equations are then analyzed to estimate the parameters for the instability that results in the formation of ripples on the bed. The nondimensional ripple length (ratio of ripple length to sand size) increases with an increase in Shields parameter. The theoretical results have an agreement with the experimental data. © 2012 American Society of Civil Engineers.

Instability theory of sand ripples formed by turbulent shear flows

Marine sediments often contain sand-clay mixtures in widely varying proportions. This study presents the results of equilibrium scour and time variation of scour depths at circular piles embedded vertically in clay alone and sand-clay mixed beds under waves. Experiments were conducted in a wave flume with different proportions of sand-clay mixtures as bed sediments. Test results for the cases of steady current and sand alone under waves are used as references. The equilibrium scour depth reduces with an increase in clay proportion n (by weight) in a sand-clay mixture. Interestingly, the scour depth reductions for n=0.3 and 1 are almost equal, suggesting that when the clay proportion in a sand-clay mixture becomes 0.3, the sand-clay mixture behaves as if it were a clay-alone mixture, in relation to scour depths. The dependency of equilibrium scour depth on the Keulegan-Carpenter number for different n-values can be expressed by an exponential law, using different coefficients and exponents. For time variation of scour, the nondimensional timescale increases with an increase in Keulegan-Carpenter number and clay proportion. However, unlike the near-equal scour depths, timescales are quite different for n=0.3 and 1. © 2011 American Society of Civil Engineers.

Journal of Waterway, Port, Coastal and Ocean Engineering

Scour at Vertical Piles in Sand-Clay Mixtures under Waves

The time-averaged characteristics of turbulent wall-wake flows downstream of a sphere placed on a rough wall are studied. The profiles of the defect of streamwise velocity, Reynolds shear stress, and turbulence intensities exhibit some degree of similarities when they are scaled by their respective peak defect values. For the velocity defect profiles, the vertical distances are scaled by the height of the location of the half-peak velocity defect. However, for the defect profiles of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the height of the location of the half-peak Reynolds shear stress defect. The magnitudes of the peak defect of all the quantities diminish with the distance downstream of the sphere characterizing the recovery of their undisturbed profiles. Additionally, the theoretical similarity solution for the velocity defect profiles is obtained. The third-order correlations imply that in the inner layer of wall wakes, a streamwise acceleration is prevalent and associated with a downward flux, suggesting sweeps. In contrast, in the outer layer, a streamwise deceleration exists and is associated with an upward flux, suggesting ejections. The profiles of the energy budget show that the turbulent and pressure energy diffusions oppose each other. The turbulent production has a positive peak, and the pressure energy diffusion has a negative peak, indicating a large gain in turbulence production in the wall-wake flows. The quadrant analysis confirms that in wall-wake flows, sweeps are the governing mechanism resulting from an inrush of fluid streaks. The bursting events have shorter duration, but they are more frequent than those in upstream. © 2011 American Society of Civil Engineers.

Wall-Wake Flows Downstream of a Sphere Placed on a Plane Rough Wall

Results of an experimental study on the effects of bed injection (upward seepage from the permeable bed) and suction (downward seepage) on the double-averaged (DA) turbulent flow characteristics over and within the interface of flow gravel beds are presented. The DA Reynolds shear stress within the interfacial sublayer undergoes a higher damping with suction and a lesser damping with injection, as compared to that with no seepage. The form-induced stress within the interfacial sublayer has a decelerating effect with no seepage and suction and an accelerating effect with injection. The quadrant analysis suggests that within the interfacial sublayer the sweep events in flows with injection and the ejection events with suction are the primary contributors toward the Reynolds shear stress production, while both the events in flows with no seepage are equally prevalent. In the roughness sublayer (form-induced and interfacial sublayers together), the mean duration of bursting increases with suction and decreases with injection, but the bursting events become less frequent with suction and more frequent with injection. The analysis of DA higher-order moments confirms that the seepage affects the Reynolds normal stress flux, the turbulent kinetic energy (TKE) flux, and the TKE budget. A downward-upstream flux of TKE is developed within the roughness sublayer with injection; while an upward-downstream flux of TKE is prevalent over the entire flow depth with suction. The significance of this study lies on the hydrodynamic process in such a physical system that may result in modifying the flow resistance, sediment entrainment, and morphological characteristics of a streambed. Copyright 2011 by the American Geophysical Union.