A mathematical model of suspension with saltation

W. Scott, Jenny Hopwood, K. Summers

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    Abstract

    A theoretical approach to the treatment of wind erosion data, particularly from a wind tunnel, is presented. Considerations are given to the utilisation of a real data set in validation of the model, data that will be presented in a forthcoming paper. Following this, the physics of particle suspension, saltation and the turbulent boundary layer are examined. Two different mathematical models evolve: one considers only suspension, another evokes Bagnold's observation that eroding material merely shifts the velocity profile and the effect of the airborne material on the effective density of the air parcel. These produce a final, relatively simple expression that credibly fits the data of Gerety and Slingerland. A critique of the approach reveals it to be an adequate expression of the known mechanisms of suspension and saltation. Derived algebraic forms for integrated collectors show several of the same ''logarithmic power'' dependences. Importantly, the results show little influence of saltation itself on the profile. It appears that the saltation process is responsible for a feedback such that the eddy diffusion process for particle movement is effectively enhanced. The combination of an appropriate correction of the pitot data (following Scott and Carter) and a complete mass balance has removed the ''kink'' from the velocity profile and also the need to consider the saltation process itself in the particle mass balance.
    Original languageEnglish
    Pages (from-to)1-22
    JournalActa Mechanica
    Volume108
    Issue number1-4
    DOIs
    Publication statusPublished - 1995

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    Scott, W., Hopwood, J., & Summers, K. (1995). A mathematical model of suspension with saltation. Acta Mechanica, 108(1-4), 1-22. https://doi.org/10.1007/BF01177324