The Planetary Boundary Layer above a Change in Surface Roughness

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  • 1 Dept. of Mathematics, University of Toronto, Canada
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Abstract

A mixing length model is used to relate the turbulent shear stress to the mean velocity field within the planetary boundary layer above a change in surface roughness under conditions of neutral thermal stability. This model gives rise to a parabolic system of partial differential equations. Numerical solutions are given for the case of flow above a step change in surface roughness across a line perpendicular to the geostrophic wind direction. These results show that a very long fetch is required for a true equilibrium flow to exist above the new, downwind surface. In particular, the surface wind direction adjusts only slowly to the new conditions. This suggests that experimental observations of the angle between the surface and geostrophic wind directions in supposedly nondeveloping flows may well have been affected by surface roughness changes well upstream of the experimental site. Some comparisons are made with numerical results for internal boundary layers within the shallower surface layer of the atmosphere.

Abstract

A mixing length model is used to relate the turbulent shear stress to the mean velocity field within the planetary boundary layer above a change in surface roughness under conditions of neutral thermal stability. This model gives rise to a parabolic system of partial differential equations. Numerical solutions are given for the case of flow above a step change in surface roughness across a line perpendicular to the geostrophic wind direction. These results show that a very long fetch is required for a true equilibrium flow to exist above the new, downwind surface. In particular, the surface wind direction adjusts only slowly to the new conditions. This suggests that experimental observations of the angle between the surface and geostrophic wind directions in supposedly nondeveloping flows may well have been affected by surface roughness changes well upstream of the experimental site. Some comparisons are made with numerical results for internal boundary layers within the shallower surface layer of the atmosphere.

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