Flow characteristics in the urban roughness sublayer (URSL) largely determine the rate at which, for example, pollutants are transported from the canopy layer. More generally, URSL characteristics set the lower boundary condition for mesoscale numerical simulations. Owing to the complexity of urban surface form and its poorly understood relation to URSL structure, generally applicable models that accurately capture the mechanisms of URSL transport are currently lacking.

Elements of a physically tenable modeling strategy for URSL transport are presented. The physical basis for this strategy is that the URSL is perhaps best defined as the region between the nominal building height and the undisturbed ASL in which the vorticity field is modified by the separated wake vorticity shed from building arrays and/or ejected from the canopy layer. The significance of this notion is brought into focus through the tensor identity,

and the assumption that at high Reynolds number there is a wide disparity between the spectral peaks associated with the velocity and vorticity fluctuations. The above equation indicates that the primary contributions to the time averaged vertical gradient of the Reynolds stress results from the difference between <ww_y> and <vw_z> velocity vorticity correlations. The substantial scale separation between the velocity and vorticity fields at high Reynolds number confines their spectral overlap (i.e., the motions contributing to the correlation) to a relatively narrow frequency range. Spatially and temporally resolved ww_y measurements in a wind tunnel and over homogeneous terrain indicate that i) the peak in the inner normalized ww_y spectral function exhibits only a very modest shift to lower frequencies over three orders of magnitude variation in Reynolds number, ii) at high Reynolds number there is a wide disparity between the peak in the w velocity spectral function and the peak in the w_y vorticity spectral function, and iii) the ww_y spectral function closely corresponds to that for w_y alone. The first result indicates that relative to the integral scales of the flow, the motions responsible for vertical stress transport become very small at high Reynolds number. The second result confirms the modeling assumption mentioned above. The last result indicates that Reynolds stress gradients are generated by motions that are primarily in the frequency range dictated by the spectral content of the contributing vorticity component.

Scaling arguments proposed by Taylor (1932) are used to convert a reduced form of the above equation into a model equation that contains the physics of gradient transport and transport due to change of scale effects. Relative to URSL transport, the primary assertion underlying the model suggests that change of scale effects should be significant if not predominant. The model requires specification of a characteristic velocity and a length scale distribution that varies with height. Based on physical grounds, the length scale function should correlate with the spectral overlap of the velocity and vorticity components contributing to the vertical stress gradient. Spatially and temporally resolved measurements in a high Reynolds number boundary layer over small scale distributed roughness and from the Mock Urban Setting Test (i.e., in an idealized but near-full scale roughness sublayer) are used to explore this issue by examining the spectral features of ww_y.