Mixing of a passive scalar in an urban-street canyon

Abstract

Mixing refers to the homogenization of a scalar field. Although it is an important subject in fluid dynamics, mixing has not attracted much attention in the urban air quality literature, where processes such as dispersion and ventilation have been highlighted. For certain applications (e.g. the accidental release of toxic chemicals), however, knowledge of the mixing rate is extremely useful. This work investigates the mixing of a passive scalar in a unit-aspect-ratio street canyon. Using large-eddy simulation, the mixing rate is characterised using the decay rate of the variance. The mixing is inhomogeneous and strongly influenced by the mean circulation; the evolution is qualitatively distinct within (i) the central vortex; (ii) corners excepting the upper downwind one; (iii) remaining regions. For each region, separate regimes related to advection and mixing can be discerned. Following established theoretical predictions, the mixing rates are related to the divergence of Lagrangian trajectories (Lyapunov exponent) and Peclet number. On account of the open boundary and inhomogeneous mixing, sensitivity of the scalar field to the initial conditions persists in the long-time limit.