The boundary layer over the urban canopy is almost always in a state of dis-equilibrium, due to the strong heterogeneities and limited fetch encountered in most urban areas. Even in very regular obstacle arrays, the mean flow and turbulence profiles exhibit large variability due to the local flow fields around the obstacles. It is possible to remove much of this spatial variability by averaging over a unit area around the obstacles, so that the profiles become a function mainly of the distance x from the front of the array. When this is done it is found that the (averaged) canopy portion of the profiles adopts very quickly to a near-equilibrium form upon encountering a large array of obstacles. However the internal boundary layer above the obstacles is a still developing flow which does not satisfy the requirements for inertial sub-layer scaling until very large fetches, rarely achieved in practice. As a result, the typical profile methods for evaluating the friction velocity (ustar) are not really applicable, and there is considerable disagreement between the ustar values measured from these profile methods and the ustar obtained form surface drag or Reynolds stresses. The question remains, how does one parameterize this flow field and make best use of the information available?

In this study we have used acoustic Doppler velocimetry in a hydraulic flume to measure the Reynolds stresses in several types of obstacle arrays, consisting of simple cubes, flat plates and elongated solids in square and staggered arrangments. It is found that for finite length arrays, the profile methods yield unusually large ustar estimates. However, it is possible to relate these ustar values to the "correct" ustar obtained directly from the measured Reynolds stresses. The two only become equal at very large fetch, but the ratio between the two (phi) is a smooth function of fetch that it should be possible to estimate. This behaviour was analyzed years ago in the literature relating to smooth-to-rough transitions, but it has never been incorporated in the analysis of flow over arrays of large obstacles with finite displacment height.

In addition to identifying the underlying relationships between the different ustar values, some very simple scaling rules have been found for the turbulence components in the non-equilibrium roughness layer when they are scaled with local values of ustar obtained from the Reynolds stresses. This means that the Reynolds stress, lateral, and vertical velocity variances can be estimated immediately from a simple measurement of the longitudinal velocity variance.