Anisotropy and multifractal analysis of turbulent velocity and temperature in the roughness sublayer of a forested canopy

Abstract

Anisotropy and multifractality in velocity and temperature time series sampled at multiple heights in the roughness sublayer (RSL) over a boreal mixed-coniferous forest are reported. In particular, a turbulent-stress invariant analysis along with a scalewise version of it are conducted to elucidate the nature of relaxation of large-scale anisotropy to quasi-isotropic states at small scales. As the return to isotropy is linked to nonlinear interactions and correlations between different fluctuating velocity components across scales, we study the velocity and temperature time series by using multifractal detrended fluctuation analysis and multiscale multifractal analysis to assess the effects of thermal stratification and surface roughness on turbulence in the RSL. The findings are compared so as to quantify the anisotropy and multifractality ubiquitous to RSL turbulent flow. As we go up in the RSL, (a) the length scale at which return to isotropy commences increases because of the weakening of the surface effects and (b) the largest scales become increasingly anisotropic. The anisotropy in multifractal exponents for the velocity fluctuations is diminished when we use the extended-self-similarity procedure to extract the multifractal-exponent ratios.