## 1 Introduction

[2] Sediment transport in rivers, estuaries, and aeolian environments represents one of the major challenges to engineers and researchers in the field of earth surface dynamics. Of specific interest is the accurate identification of the flow conditions near the threshold of movement. This has a wide range of applications from stable channel design to establishing acceptable flushing flow rates downstream of reservoirs.

[3] A number of diverse theories have been proposed in an attempt to relate flow strength, expressed by means of a certain flow parameter or derivatives of it, to the resulting rates of sediment transport. These theories can be classified into two basic categories, depending on the fundamental laws of physics they rely on.

[4] The first approach, based on Newton's laws of motion, uses vectorial quantities such as mean stream velocity (*U*) [*Hjulström*, 1939] or *Shields*’s [1936] parameter, *τ* = τ*/[*g*(*ρ _{s} − ρ_{f}*)

*D*] (where

_{50}*τ*is the boundary shear stress,

*g*the acceleration of gravity,

*D*the bed material median size, and

_{50}*ρ*and

_{f}*ρ*the density of fluid and sediment, respectively). This approach is widely used for identifying flow conditions near incipient movement despite the criticism it has received in the literature [

_{s}*Miller et al.*, 1977;

*Bettess*, 1984;

*Buffington and Montgomery*, 1997;

*Shvidchenko and Pender*, 2000;

*Paphitis et al.*, 2002].

[5] The second approach is linked to the laws of thermodynamics, trying to correlate the scalar variables of energy or its derivative quantities to the rate of entrainment of sediment. One of the first attempts to emphasize the role of “stream energy” on sediment discharge can be found in the classical work of *Gilbert* [1914]. Gilbert specified that the rate of expenditure of available potential energy between two stations of different elevation equals the product *QSg*, with *Q* the water discharge and *S* the bed slope. Since then, power theories have been related to the rate of expenditure of kinetic energy of the stream or of available potential energy (gravitational power) to transport sediment by a number of researchers [*Rubey*, 1933; *Knapp*, 1938; *Bagnold*, 1956]. However, it was not until the work of *Bagnold* [1966] that this concept was extended to develop quantitative equations for the prediction of total sediment concentration. *Bagnold* [1966] introduced the concept of specific stream power, *ω* = *Q S g/b*, with *b* the width or hydraulic perimeter of the stream, as the rate of the stream's energy supply per unit area or simply as the product *U τ* [*Bagnold*, 1977, 1980, 1986]. *Yang* [1972] hypothesized that unit stream power, defined as the rate of expenditure of potential energy per unit weight of water and given by the product of mean flow velocity and energy slope, *U S*, is the pertinent quantity controlling the concentration of suspended sediment, bed load, or total sediment discharge as verified from statistical analysis of experimental data [*Yang*, 1972, 1979; *Yang and Stall*, 1976; *Yang and Molinas*, 1982].

[6] Both traction and power approaches usually use temporally and sometimes spatially averaged quantities such as mean velocity, bed shear stress, or their product. Such mean quantities fail to capture the effect of rapidly fluctuating hydrodynamic forces on the entrainment of bed material. Particularly for the rough turbulent flow regime (e.g., boundary Reynolds number, * R_{*}* [

*=u*] >100, with

_{*}D_{50}/ν*u*the shear velocity, and

_{*}*ν*the kinematic viscosity of water), Shields's criterion for inception of motion of coarse particles shows scatter of more than an order of magnitude [e.g.,

*Buffington and Montgomery*, 1997;

*Lavelle and Mofjeld*, 1987]. Many researchers acknowledging the limitations of the above criteria, particularly for near-critical flow conditions, have emphasized the significance of the magnitude of peaks in the instantaneous hydrodynamic forces in the vicinity of the boundary [

*Einstein and El-Samni*, 1949;

*Sutherland*, 1967;

*Paintal*, 1971;

*Apperley and Raudkivi*, 1989;

*Papanicolaou et al.*, 2001;

*Sumer et al.*, 2003;

*Zanke*, 2003;

*Hofland et al.*, 2005;

*Schmeeckle et al.*, 2007;

*Vollmer*

*and Kleinhans*, 2007;

*Dwivedi et al.*, 2010, 2011b]. Recently,

*Diplas et al*. [2008] demonstrated the importance of duration of flow events above a critical level of the instantaneous stress tensor and suggested their product, impulse, as the criterion to characterize incipient motion conditions.

*Valyrakis et al*. [2010] extended the proposed impulse criterion over a wide range of grain mobility levels for both saltating and rolling particles. The validity of the impulse concept and the results of the theoretical formulation were demonstrated through a series of appropriately designed experiments [

*Diplas et al.*, 2008;

*Valyrakis et al.*, 2010].

[7] In this study, a new criterion for particle entrainment linking the available energy of turbulent flow events to the mechanical work required for grain entrainment is proposed for both pure saltation and rolling. The energy approach to grain dislodgement, although directly linked to the impulse criterion, is demonstrated to be more versatile and intuitive. The validity of the proposed criterion is examined through the detailed analysis of data obtained from flume experiments corresponding to low-mobility conditions.