Using a data correlation for the wall stress associated with very rough boundaries and a semi-empirical calculation method, the shape of boundary layers in exact equilibrium with the roughness beneath them is calculated. A wide range of roughness geometries (two- and three-dimensional elements) is included by the use of equivalent surfaces of equal drag per unit area. Results can be summarized in a single figure which relates the shape factor of the boundary layer (its exponent if it has a power law velocity profile) to the height of the roughness elements and their spacing. New data for one turbulent boundary layer developing over a long fetch of uniform roughness is presented. Wall shear stress, measured directly from a drag plate is combined with boundary layer integral properties to show that the shear stress correlation adopted is reasonably accurate and that the boundary layer is close to equilibrium after passing over a streamwise roughness fetch equal to about 350 times the roughness element height. An example is given of the way in which roughness geometry may be chosen from calculated equilibrium results, for one particular boundary layer thickness and a shape useful for simulating strong atmospheric winds in a wind tunnel.

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