Suspension transport of wind‐eroded sand particles

Sand‐sized particles occupy the region 0 S x, z < CQ in a 2‐D space in which x is horizontal and z vertically upwards. An airstream U = [U (z), 01 blows through the region. The sand particles are then subject to advection, diffusion and sedimentation by gravity. The equation governing the concentration c(x, z) of the sand is studied in the presence of the boundary conditions that (i) the concentration of sand at x = 0 is a prescribed function of z [F (z), say] and (ii) the concentration is assumed to decay to zero as x tends to infinity. Condition (i) is realized physically when an experimental station for measuring the concentration c(0, z) with height is set up at x = 0. When U (z) = pzm, where p and m are constants, a solution c(x, z) is obtained in closed form for general profiles F (z). The general characteristics of c(x, z) in the region 0 I x 5 co are examined for all z. It is found that for fixed x > 0, c(x, z) decays with z on a length scale (i.e. a unit of distance) which depends on m and not on 0. For fixed z, on the other hand, c(x, z) decays on a horizontal length scale X which depends on p and m as well as on the friction velocity. The concentration decays algebraically to zero as X tends to infinity.