Turbulence anisotropy in unstable stratified flows over hills: an idealized large eddy simulation study

Turbulent characteristics of the atmospheric surface layer are considered to be well understood over flat and horizontally homogeneous terrain. There, their initial description was provided by the Monin and Obukhov Similarity Theory (MOST; 1954) and fine-tuned using data from targeted observational campaigns (e.g., Businger et al., 1971). Since then, MOST has served as the basis for parameterization of turbulent exchange in numerical models and for processing of near-surface weather observations. Over complex heterogeneous terrain, however, classical MOST is not applicable due to violation of its underlying assumptions, and has been shown not to work. The recent work of Stiperski and Calaf (2023) has offered a way forward for turbulence parametrizations over non-ideal terrain, and has shown that MOST can be improved if the degree of turbulence anisotropy of the Reynolds stress tensor is included as an additional nondimensional parameter. From practical point of view, this raises a demand to parameterize the turbulence anisotropy over complex terrain for a possibly wide range of boundary-layer conditions.

The current study uses large eddy simulation technique to explore the impact of infinite sinusoidal topography on turbulence anisotropy in neutral and unstably stratified flows. The parameter range explored covers a range of hill heights and length scales, as well as geostrophic winds speeds, while the simulations are initialized with a constant surface heat flux. Simulations are carried out using the pseudo-spectral NCAR model with terrain-following coordinates (Sullivan et al., 2014).  The hill height is kept low due to the incompressible nature of the flow. As the model utilizes the MOST itself at the lower boundary, the simulations require very high-resolution to resolve a wide fraction of the inertial-range. Moreover, turbulence statistics are explored at a distance from the surface.