Quantifying Three-dimensional Topological Dispersion within Realistic Urban Canopies using Magnetic Resonance Imaging

Scalar dispersion within urban canopies is governed by topological dispersion due to the mean flow around buildings and turbulent dispersion due to eddies. Topological dispersion can be important in the near-field of ground level sources, because complex mean flow patterns can produce cross-wind or even up-wind plume spread. However, a 3D understanding of the flow topology in realistic urban canopies is relatively limited. In this work, magnetic resonance imaging is used to measure the 3D mean velocity and concentration fields in a scale model of Oklahoma city based on the JU2003 field tests. Transport boundaries, defined as 2D manifolds with small mean scalar flux across them, are extracted using the Finite Time Lyapunov Exponent (FTLE) field and correlated to the dispersion patterns. Ridges of the backwards FTLE field, which identify hyperbolic manifolds exhibiting exponential convergence of fluid trajectories, act as barriers to scalar transport that redirect the plume. The MRI measurements enable a 3D characterization of transport boundary topology and explain observed cross-wind and vertical scalar transport behavior. Remarkably, although the FTLE field only guarantees small mean scalar flux across a ridge, the structures appear robust to turbulent mixing.