Abstract
The power law and logarithmic law among others are the most commonly well-known theories for equilibrium mean profile of dust concentration in a neutral atmospheric surface layer. However, these theories are based on the assumption of homogeneity in horizontal (streamwise) direction, thereby the horizontal advection term in the transport equation is neglected. In this study, with the help of a self-similar analytical solution of the two-dimensional steady-state dust transport equation (Chamecki and Meneveau, J Fluid Mech 683:1–26, 2011), we examine the applicabilities of the assumption which the one-dimensional theories are based on. In addition, we also propose an empirical fit of the theory, and good agreements with reference data have been obtained. The new approximate profile can be used as an alternative of the one-dimensional theories in practical applications.
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