THEORY (cont.) - doern40003

Technical Note DOER-N4

May 1999

A method developed by Ackers and White (1973) is used to determine the water depth for initiation

of motion for a specified grain size, current condition, and wave condition. The original Ackers and

White relationships predict sediment transport and initiation of sediment transport as a function of

sediment grain size, depth, and depth-averaged current velocity. As stated previously, this method

was designed for current-only environments, and the above described effective velocity that

accounts for waves and currents will be substituted for the current velocity in all equations. The

equations were not developed for a single grain size, but rather for uniformly graded noncohesive

sediment with a median grain diameter in the range of 0.04 mm to 4.0 mm, assuming only a small

fraction (<5-17 percent depending on mineralogy) cohesive clays and fine silts (White 1972). Many

equations have been developed to describe noncohesive sediment transport, and the various

methods have been compared with multiple data sets (Brownlie 1981). These comparisons indicate

that the Ackers and White method performs as well or better than the other well-recognized

procedures.

The Ackers-White transport equations relate initiation of sediment transport to two dimensionless

quantities. The first, a nondimensional grain size Dgr , is defined as a function of the ratio of the

immersed particle weight to the viscous forces acting on the grain:

 g (s - 1)

Dgr = D 



(7)

υ2 



where

D = sediment diameter (i.e., D50), ft

g = acceleration of gravity, ft/sec

s = sediment-specific gravity

υ = fluid kinematic viscosity, ft2/sec

The value of Dgr is used to categorize the sediment as coarse or transitional, with the following

coefficients defined for the two sediment classifications:

a. Coarse sediments: Dgr > 60.

n = 0.0

A = 0.17

b. Transition sediments: 1.0 < Dgr ≤ 60.0.

()

n = 1.00 - 0.56 log Dgr

(8)

0.23

+ 0.14

(9)

Dgr