A Phenomenological Model for Wind Speed and Shear Stress Profiles in Vegetation Cover Layers

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Abstract
A phenomenological model for the mean wind speed and Reynolds shear stress profiles with height in a vegetation cover layer is derived from forms suggested by truncation of the equations of turbulent fluid motion at second order in fluctuating velocity products. The initial formulation is unique in that the force per unit volume resisting fluid motion is treated as a body force having a height-dependent character. The body force is assumed to be proportional to the instantaneous speed squared and in the opposite direction from the instantaneous velocity. Viscous forces are ignored as are all pressure forces except for a steady vertical pressure gradient. Closure of the, equations is effected by a phenomenological assumption linking the static pressure and the square of the mean wind speed. The mean wind speed profile predicted by the model is an exponential in the cumulative drag area per unit planform area as a function of height, which is a simple exponential in height for cover with uniform pl... Abstract A phenomenological model for the mean wind speed and Reynolds shear stress profiles with height in a vegetation cover layer is derived from forms suggested by truncation of the equations of turbulent fluid motion at second order in fluctuating velocity products. The initial formulation is unique in that the force per unit volume resisting fluid motion is treated as a body force having a height-dependent character. The body force is assumed to be proportional to the instantaneous speed squared and in the opposite direction from the instantaneous velocity. Viscous forces are ignored as are all pressure forces except for a steady vertical pressure gradient. Closure of the, equations is effected by a phenomenological assumption linking the static pressure and the square of the mean wind speed. The mean wind speed profile predicted by the model is an exponential in the cumulative drag area per unit planform area as a function of height, which is a simple exponential in height for cover with uniform pl...

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