Climatologies of Anisotropy in the Reynolds Stress Tensor

Turbulent mixing processes in the atmospheric boundary layer are usually described using Monin-Obukhov similarity theory (MOST), which combines the mean flow properties in the dimensionless stability parameter. Originally, this theory was derived for steady flows over flat surfaces and fails to describe turbulence under unsteady conditions or in complex terrain. However, recent research showed that the inclusion of geometric properties of the Reynolds stress tensor can help to overcome this problem. From the eigenvalues of the Reynolds stress tensor, three topological limiting cases (one-, two- and three-component) can be derived, where the three-component limiting state describes isotropic turbulence. Additionally including a measure of the deviation from isotropy, i.e. anisotropy, to MOST reduces the scatter of observations around the parametrized stability correction function and thereby improves MOST. However, general climatologies of anisotropy based on eddy-covariance measurements have not been studied so far.
Based on long-term eddy-covariance measurements in Finse, an alpine valley in southern central Norway, the seasonality and diurnal variation of anisotropy is investigated. It is shown that the flow is more anisotropic in winter than in summer. In winter, the wave-dominated one-component limiting state dominates at night and the two-component limiting state dominates during the day. In summer, the flow becomes more isotropic during the day. Correlation analysis shows that anisotropy correlates mainly with wind speed shear. Compared to the two-component limiting state, the one-component limiting state occurs more frequently with a high intermittency factor.
In addition, flux tower measurements from the FLOSS2 experiment are used to study climatologies of the vertical profiles of anisotropy. It is shown that turbulence is strictly anisotropic near the ground and becomes more isotropic with height. During the day, the flow tends towards the two-component limiting state near the ground and from about 10 m altitude towards the three-component limiting state. At night, the one-component limiting state dominates, especially at higher altitudes.
Such climatologies of anisotropy and their relation to large-scale meteorological variables can help in the development of new parametrizations for numerical weather prediction models.