Snyder, William and Castro, Ian P.
The critical Reynolds number for rough-wall boundary layers
Journal of Wind Engineering and Industrial Aerodynamics, 90, (1), . (doi:10.1016/S0167-6105(01)00114-3).
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Rough-wall boundary layers become aerodynamically smooth if the ‘roughness Reynolds number’ Re*=u*z0/? becomes sufficiently small. Conventional wisdom is that Re* should exceed at least two and perhaps be as much as five before viscous effects are insignificant. This criterion is assessed for the types of rough wall commonly used in laboratory simulations of atmospheric boundary layers—arrays of sharp-edged obstacles with significant separation between each obstacle. It is demonstrated that for such surfaces the roughness length z0 remains constant for falling roughness Reynolds numbers down to at least Re*=1. Viscous effects are shown to change the near-wall Reynolds stresses only for Re* below similar values, so that z0-scaling (rather than scaling based on ?/u*) remains appropriate down to at least Re*=1. One of the practical implications of this result is that wind-tunnel simulations of atmospheric boundary layers can be successful at lower wind speeds (or with smaller roughness elements) than previously supposed.
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