Interpreting Turbulence Anisotropy in a Streamline Coordinate System

Mixing and transport in the atmospheric boundary layer are a result of the anisotropic nature of turbulence. Recently the inclusion of anisotropy of the Reynolds stress tensor into similarity theory of near-surface turbulence has been proposed. Anisotropy is quantified through the eigenvalues of the anisotropy tensor, which can be visualized by geometric shapes. We conduct a systematic investigation of velocity variances and covariances conditional to this geometric shape with the purpose of identifying common patterns. We discuss the influence of eigenvectors' directions on turbulent transport in relation to the streamline coordinates defined along the mean wind vector. Eigenvectors' direction identifies the orientation of anisotropic shapes, and this geometric approach is meant to investigate if physical constraints on orientation exist, as these could inform turbulence parameterizations. Two data sets are used for the analyses, one from a relatively flat terrain and one from a glacier site. Results show that it is not possible to identify a unique orientation for each anisotropy. Geometric shapes span a broad range of inclinations in the vertical, not strongly constrained by height or atmospheric stability. However, anisotropic turbulence is shown to have shallower inclination than isotropic turbulence. One-component states, ubiquitous under stable stratification, are well described by the orientation of the dominant eigenvector in the horizontal, characterized by large horizontal covariance, or large variance which aligns anisotropy in the streamwise/spanwise direction. Results highlight that the geometric orientation of turbulence may depend on the site and future investigations will include geometric parameters characterizing the orography in the analyses.