Scale-by-scale analysis of stratified turbulence using DNS and WRF simulations

The increase in greenhouse gas emissions from human activities are driving a continuous rise in Earth’s temperature. The atmosphere is a highly complex system: it is vertically stratified, composed of layers with distinct flow characteristics, involves energy exchanges in both horizontal and vertical directions, exhibits heterogeneous composition, and is turbulent over a wide range of spatial and temporal scales. A detailed understanding of stratified turbulence and its role in climate dynamics is therefore essential.

Climate models necessarily rely on assumptions, either by explicitly resolving large-scale dynamics while parameterizing small-scale processes, or by focusing on small-scale turbulence with simplified representations of large-scale flows. To better understand the interactions across scales, we perform a scale-by-scale analysis based on structure functions for idealized Direct Numerical Simulation (DNS) and for Weather Research and Forecasting (WRF) model outputs.

While deriving the governing equations from both DNS and WRF datasets, second-, third- and fourth-order structure functions are computed in two-dimensions. Firstly, along the z-axis for DNS and WRF, in the direction of stratification, and secondly, in the plain perpendicular to z-axis (perpendicular to the surface). Despite differences in model complexity and scales, both datasets exhibit similar statistical behavior across orders.

The two-dimensional structure functions shows: a 90° reflection symmetry when averaging over space and time, while a 180° rotational symmetry is observed when averaging over space at each time step. Furthermore, the third-order structure function reveals a direct energy cascade aligned with the mean flow direction and an inverse energy cascade in the direction perpendicular to the mean flow. These features are consistent across both datasets and are in agreement with previous experimental observations from academic flows.

Future work will focus on separating wave-like motions, such as gravity waves, from the turbulent component in DNS and WRF outputs. This decomposition will give a clearer assessment of the respective roles of waves and turbulence in scale-by-scale energy transfers, and will help the interpretation of structure function analyses in stratified atmospheric flows.