Equilibration of saltation

A two‐dimensional numerical model of the saltation process was developed on a parallel computer in order to investigate the temporal behaviour of transport rate as well as its downwind distribution. Results show that the effects of unsteady flow on the transportation of particulates (sediment) have to be considered in two spatial dimensions (x, y) . Transport rate Q(x, t) appears in the transport equation for mass M(x, t) :${1 \over A} {\partial M \over \partial t}= - {\partial Q \over \partial x} + S$ where A = Δ xW denotes unit area composed of unit streamwise length Δ x and width W . S(x, t) (units kg m −2 s −1 ) stands for the balance over the splash process. A transport equation for transport rate itself${\partial Q \over \partial t}= - U_{c} {\partial Q \over \partial x} - Q {\partial U_{c} \over \partial x} + {\partial \over \partial t} (\Delta x S)$ is suggested with U c ( x , t ) a mean particle velocity at location x as the characteristic velocity of the grain cloud. For a steadily blowing wind over a 50 m long sediment bed it was found that downwind changes in Q cease after roughly 10–40 m, depending on the strength of the wind. The onset of stationarity (∂/∂ t =0) was found to be a function of the friction velocity and location. The local equilibrium between transport rate and wind was obtained at different times for different downstream locations. Two time scales were found. One fast response (in the order of 1) to incipient wind and a longer time for equilibrium to be reached throughout the simulation length. Transport rate also has different equilibrium values at different locations. A series of numerical experiments was conducted to determine a propagation speed of the grain cloud. It was found that this velocity relates linearly to friction velocity. Copyright © 2000 John Wiley & Sons, Ltd.