COMPUTATIONAL MODEL (cont.)

ERDC TN-DOER-E10

April 2000

∆T = time-step

= settling velocity of particle class i

Wsi

Lx,Ly,Lz

= particle diffusion distance in the x-, y-, z-directions, respectively

Particle diffusion is assumed to follow a simple random walk process. A diffusion distance defined

as the square root of the product of an input diffusion coefficient and the time-step is decomposed

into X and Y displacements via a random direction function. The Z diffusion distance is scaled by

a random positive or negative direction. The equations for the horizontal and vertical diffusion

displacements are written as:

Lx = Dh ∆T cos 2πR

(7)

Dh ∆T sin b2πRg

Ly =

(8)

Lz = Dz ∆T 0.5 - R

(9)

where

Dh,Dz = horizontal and vertical diffusion coefficients, respectively

R = random real number between 0 and 1

The particle model allows the user to predict the transport and fate of classes of settling particles,

e.g., sands, silts, and clays. The fate of multicomponent mixtures of suspended sediments is

predicted by linear superposition. The particle-based approach is extremely robust and independent

of the grid system. Thus, the method is not subject to artificial diffusion near sharp concentration

gradients and is easily interfaced with all types of sediment sources. For example, although the

basic purpose of SSFATE is to aid in answering questions concerning the need for environmental

windows associated with a dredging operation, models such as STFATE (Short-Term FATE)

(Johnson and Fong 1995), which computes the near field dynamics of a placement operation, could

be used to provide the sediment source associated with placement operations. In addition, under the

Dredging Operations and Environmental Research (DOER) Program, a near field model is being

developed to answer mixing zone questions connected with the placement of dredged material by

a pipeline. Plans call for implementing results from the pipeline model as a sediment source in

SSFATE.

Equations 4-6 show that the components of the ambient current field are required to transport the

sediment particles. SSFATE provides two options for the user. The simplest option is to input

limited field data, e.g., the magnitude of the tidal current, its period, and its principal direction. An

interpolation scheme described by Cressman (1959) is then employed to "paint" a flow field over

a rectangular water-land numerical grid. This flow field is then used to provide the (U, V)

components of the ambient current in Equations 4 and 5. With this option, there is no vertical

component of the flow field. The second option is for the user to import a time-varying,