Estimating Drag Coefficients for Dense Vegetation Canopies

Abstract:

For vegetation canopies of sufficient density, the effect of canopy elements on the flow can be parameterized as a distributed drag calculated as the product of the square of velocity, the canopy density and a drag coefficient. The high-order turbulence statistics are sensitive to the dependence of drag coefficient on velocity, and therefore an accurate drag coefficient model is critical for large-eddy simulation (LES) models to reproduce the structure of turbulence and the transport of scalars within and above the canopy. For statistically stationary flows over a horizontally homogeneous canopy, the mean canopy drag balances the vertical gradient of mean vertical momentum flux and the streamwise mean pressure gradient. Direct measurements of the pressure gradient are unavailable for terrestrial canopies, and thus traditional estimates of the mean drag are only reliable for the upper canopy region, where the streamwise mean pressure gradient is negligible in the force balance. In this work, a practical approach is proposed to fit the streamwise mean pressure gradient, which then provides reliable estimates of the mean drag for the lower canopy region. The resulting relationship between a preliminary estimate of the drag coefficient and the characteristic velocity scale resembles the imposed drag coefficient models. Starting from the preliminary estimate, iterative approaches are proposed for drag coefficient models following a power-law or a capped power-law of velocity, which represent the effect of bending and streamlining of flexible canopy elements. Compared with the traditional approach that typically underestimates the power-law exponent by 20%--40%, the iterative approaches require the same input data (i.e., instantaneous velocity obtained at grids that are sufficient to resolve the vertical gradient of mean vertical momentum flux within the canopy), but yield remarkable improvement in estimating the drag coefficients.