Two-dimensional scalar spectra in the deeper layers of a dense and uniform model canopy

The turbulent flow inside dense canopies is characterized by wake production and short-circuiting of the energy cascade. How these processes affect passive scalar concentration variability in general and their spectral properties in particular remains a vexing problem. Progress on this problem is frustrated by the shortage of high resolution spatial concentration measurements, and by the lack of simplified analytical models that connect spectral modulations in the turbulent kinetic energy (TKE) cascade to scalar spectra. Here, we report the first planar two-dimensional scalar concentration spectra (phi(cc)) inside tall canopies derived from flow visualization experiments. These experiments were conducted within the deeper layers of a model canopy composed of densely arrayed cylinders welded to the bottom of a large recirculating water channel. We found that in the spectral region experiencing wake production, the phi(cc) exhibits directional scaling power laws. In the longitudinal direction (x), or the direction experiencing the largest drag force, the phi(cc)(k(x)) was steeper than k(x)(-5/3) and followed an approximate k(x)(-7/3) at wavenumbers larger than the injection scale of wake energy, where k(x) is the longitudinal wavenumber. In the lateral direction (y), the spectra scaled as k(y)(-5/3) up to the injection scale, and then decayed at an approximate k(y)(-7/3) power law. This departure from the classical inertial subrange scaling (i.e., k(-5/3)) was reproduced using a newly proposed analytical solution to a simplified scalar spectral budget equation. Near the velocity viscous dissipation range, the scalar spectra appear to approach an approximate k(-3), a tantalizing result consistent with dimensional analysis used in the inertial-diffusive range. Implications to subgrid modelling for large-eddy simulations (LES) inside canopies are briefly discussed.