Degree Name

Master of Engineering - Research


School of Civil, Mining and Environmental Engineering


This study investigates turbulence characteristics in steady and unsteady non-uniform flows and how these flows affect the incipient motion of sediment transport. Specifically, it deals with two issues, one relates to the deviation of critical shear stress in non-uniform flow from that in Shield diagram, and the other is associated with the deviation of mean velocity profile and other turbulence characteristics in steady and unsteady non-uniform flows from the classical Log law or other their predictions in uniform flow. New formulas have been developed for the determination of critical shear stress and the prediction of longitudinal velocity and other turbulence characteristics, such as vertical velocity, Reynolds shear stress and turbulence intensities across the water depth in uniform and non-uniform (steady and unsteady) flows.

The deviation of critical shear stress from Shields diagram is often attributed to many factors like measurement errors, sediment gradation/shapes, or channel-bed slopes, but little attention has been paid to the effect of vertical velocity that could be caused by a non-uniformity, seepage or unsteadiness etc. This part has re-examined the measured data available in the literature and found that, the vertical velocity in a channel flow also leads to the deviation of critical shear stress from the standard Shield’s diagram. A closer look of the measured data shows that positive/negative deviation of measured critical shear stress from Shields’ prediction corresponds to the up/downward vertical velocity; the Shields diagram is valid only when the flow is uniform. A new theory for critical shear stress has been developed, which shows that the decelerating flows promote the mobility of sediment, but accelerating flows constrain its mobility. A unified critical Shields stress for sediment transport has been established, that can predict the critical shear stress for the initial motion of sediment in both uniform and non-uniform flows.

This study also investigates the deviation of measured mean horizontal velocity profile from the classical Log law. The Log law is applicable in the inner region where y / h < 0.2 when compared with the measured longitudinal velocity. However, in the rest of water depth i.e. y / h ≥ 0.2, the measured horizontal velocity profile deviates from its prediction using Log law. The deviation is negative when the flow is accelerating, or the measured longitudinal velocity profile fall below the Log law; the deviation becomes positive when the flow is decelerating, or the measured longitudinal velocity profile has higher value than the Log law. The reason for this deviation is attributed to the positive or negative value of flow acceleration generated from accelerating or decelerating non-uniform flows, respectively. For this reason, different empirical equations have been established to predict longitudinal velocity in accelerating and decelerating steady and unsteady flows depending on the dimensionless flow acceleration. Based on these developed equations, Log law, Cole’s Wake law and Dip law have been combined together to predict the mean velocity profile in uniform and non-uniform steady and unsteady flows across the full depth of a channel. This modification has been confirmed based on experimental data sets available in the literature for both steady and unsteady flows, and a reasonable agreement between the measured and predicted mean velocity profile is obtained.

In a similar manner, new formulas to express the profiles of other turbulence characteristics, such as Reynolds shear stress, turbulence intensities and vertical velocity have been developed for both steady and unsteady non-uniform flows. The newly proposed equations are also dependent on the impact of flow acceleration on the deviation of these turbulence characteristics from those in uniform flow. The validity of these proposed equations has been verified using published experimental data for smooth and rough rectangular open channels and good agreement between the predicted and observed profiles has been achieved. Based on these developed formulas, the turbulence characteristics in unsteady flow can be easily estimated because the time factor is not included.

In this study, another method to estimate the turbulence intensities profiles in unsteady flow has been found. This prediction depends on the ratio of Reynolds shear stress in non-uniform flow to that in uniform flow. Two empirical equations have been proposed to express the relationship between horizontal and vertical turbulence intensities with the measured Reynolds shear stress based on experimental data available in the literature. These empirical equations are tested using the experimental data of Song (1994), Nezu et al. (1997), Song and Chiew (2001) and Emadzadeh et al. (2010), good agreements have been achieved between the measured and predicted turbulence intensities by applying these relationships.

Based on this research, a total of seven new empirical equations have been developed and verified with literature data. These relationships can be used to predict turbulent structures and sediment transport in steady and unsteady flows and these findings significantly add to the body of scientific knowledge available in this area.