The physics of sand transport by wind
The aim of this study is to develop and test a physical model of wind blown sand transport. Once established, such a model will lead to valuable insight into the physics of sand transport by wind especially the processes that interact to produce equilibrium transport conditions. The study begins with a review of the physics of wind blown sand, beginning with Bagnold (1941). In particular, four sub-processes are discussed; aerodynamic entrainment, the grain trajectory, the grain/bed collision and the modification of the wind by the grains. The physical model is based on the coupling (or interaction) of the four sub-processes. The grain/bed collision is modelled using experimental data obtained by Willetts and Rice (1985). The wind modification is calculated from the force profile exerted by the grains and the differential fluid shear stresses induced by the grains; a mixing length model is used to calculate these stresses. The results from the model are compared with the observed features of wind flow sand transport and the agreement is encouraging. Realistic wind profiles are calculated. These profiles show a marked deceleration by the grain cloud and an increase in effective roughness due to the additional drag imposed on the wind by the grains. Moreover the horizontal mass flux profile decays exponentially from the surface in accord with experimental measurements and the sand transport rate has a roughly cubic dependence on the shear velocity. Thus, the success of the model in reproducing (spontaneously) many of the observed features of wind blown sand transport encourages confidence that the physics used to construct the model is broadly correct. A further important result emerges from the model. There appears to be two time scales associated with equilibrium saltation. Firstly, the time for the grain cloud to come into equilibrium with the surface wind; this occurs over a time of approximately 1 s. Secondly, there is an increase in the effective roughness of the surface due to the additional drag imposed on the wind by the grain cloud. The atmospheric boundary layer must come into equilibrium with this change in roughness. This second equilibrium takes place over a much longer time scale of several tens of seconds or more. It results in a gradual decay of the shear stress in time after an overshoot of the steady state. It is noted that the response in time of the boundary layer to a change in roughness is analogous to its response in distance found by Jensen (1978). It is suggested, in the concluding chapter, that the spatial and temporal variation of the saltation cloud may be related through the application of Taylor's hypothesis for turbulence. The saltation modified wind is studied with the aid of an analytical wind profile derived from an assumed fluid shear stress distribution. This distribution is chosen for its similarity to the model calculated distribution: the intension being to use the analytical wind profile as a tool to investigate the model generated wind profile. From this analytical wind profile it is shown that the 'kink' in the wind profile (first noted by Bagnold (1941)) is caused by a maximum in the force profile exerted on the wind by the grains. Such a maximum is shown to exist in the force profile generated by the saltation model. Thus, it is concluded, that the 'kink' found in many experimentally measured wind profiles is likely to be caused by a maximum in the force profile exerted by the grains on the wind. This result is important because further understanding of modification of the wind will ensure that experimental measurements made are consistent with the physics of the system: in particular that wind velocity measurements used to calculate the shear velocity should be made above a height of 2-3 cm from the surface (i.e. above the kink). In the concluding section the desirability of a multiple grain size saltation model is discussed as an important step towards more realistic modelling. Further attention is directed towards modelling sand transport in gusty winds and inclusion of interaction with a developing bed.