The Turbulent Pressure Spectrum Within the Roughness Sublayer of a Subarctic Forest Canopy

Abstract

The turbulent static pressure spectrum $E_{pp}\left(k_x\right)$ as a function of longitudinal wavenumber $k_x$ in the roughness sublayer of forested canopies is of interest to a plethora of problems such as pressure transport in the turbulent kinetic energy budget, pressure pumping from snow or forest floor, and coupling between flow within and above canopies. Long term static pressure measurements above a sub-arctic forested canopy for near-neutral conditions during the winter and spring were collected and analyzed for three snow cover conditions: trees and ground covered with snow, trees are snow free but the ground is covered with snow, and snow free cover. In all three cases, it is shown that $E_{pp}\left(k_x\right)$ obeys the attached eddy hypothesis at low wavenumbers —with $E_{pp}\left(k_x\right)\propto u_{\ast }^4{k}_x^{-1}$ and Kolmogorov scaling in the inertial subrange at higher wavenumbers—with $E_{pp}\left(k_x\right)\propto {ϵ}^{4/3}{k}_x^{-7/3}$, where $u_{\ast }$ is the friction velocity at the canopy top, $ϵ$ is the mean turbulent kinetic energy dissipation rate, $z$ is the distance from the snow top, and $\delta$ is the boundary layer depth. The implications of these two scaling laws to the normalized root-mean squared pressure $C_p={\sigma }_p/u_{\ast }^2$ and its newly proposed logarithmic scaling with normalized wall-normal distance $z/\delta$ are discussed for snow covered and snow free vegetation conditions. The work here also shows that the $k_x^{-1}$ in the $E_{pp}\left(k_x\right)$ appears more extensive and robust than its longitudinal velocity counterpart.