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 <wwy> and <vwz> 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 wwy
measurements in a wind tunnel and over homogeneous terrain indicate that i)
the peak in the inner normalized wwy 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 wy vorticity spectral function, and iii) the wwy spectral function closely corresponds to that for wy 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 wwy.
Supplementary URL: