The prediction of dust erosion by wind: An interactive model

We have devised a partial differential equation for the prediction of dust concentration in a thin layer near the ground. In this equation, erosion (detachment), transport, deposition and source are parameterised in terms of known quantities. The interaction between a wind prediction model in the boundary layer and this equation affects the evolution of the dust concentration at the top of the surface layer. Numerical integrations are carried out for various values of source strength, ambient wind and particle size. Comparison with available data shows that the results appear very reasonable and that the model should be subjected to further development and testing.Notation (x, y, z, t) space co-ordinates and time (cm,t) - u, v components of horizontal wind speed (cm s^–1) - u_g, v_g components of the geostrophic wind (cm s^–1) - V=(u²+v²)^1/2 (cm s^–1) - (û v)= 1/(h – k)_k^h(u, v)dz(cm s^–1) - V_* friction velocity (cm s^–1) - z₀ roughness length (cm) - k₁ von Karman constant =0.4 - V_d deposition velocity (cm s^–1) - V_g gravitational settling velocity (cm s^–1) - h height of inversion (cm) - k height of surface layer (cm) - potential temperature (°K) - _gr potential temperature at ground (°K) - _K potential temperature at top of surface layer (°K) - P pressure (mb) - P₀ sfc pressure (mb) - C_p/C_v - (t)= /z lapse rate of potential temperature (°K cm^–1) - A(z) variation of wind with height in transition layer - B(z) variation of wind with height in transition layer - Cd drag coefficient - C_HO transfer coefficient for sensible heat - C dust concentration (g m^–3) - C_K dust concentration at top of surface layer (g m^–3) - D(z) variation with height of dust concentration - u, v, w turbulent fluctuations of the three velocity components (cm s^–1) - A₁ constant coefficient of proportionality for heat flux =0.2 - Ri Richardson number - g gravitational acceleration =980 cm s^–2 - Re Reynolds number = - D_s thickness of laminar sub-layer (cm) - v molecular kinematic viscosity of air - coefficient of proportionality in source term - dummy variable - t time step (sec) - n time index in numerical equationsOn sabbatical leave at University of Aberdeen, Department of Engineering, September 1989–February 1990.