Asymptotically reduced modeling of anisotropic coherent structures in the atmospheric Ekman boundary layer

Understanding the dynamical interactions between turbine wakes and quasi-coherent turbulent flow structures in the ambient marine atmospheric boundary layer (MABL) is crucial for optimizing offshore wind-farm power generation. As a first step toward developing computationally-efficient algorithms for predicting the ambient MABL turbulent structures, we derive an asymptotically-reduced set of PDEs, known as the boundary region equations (BRE), here augmented with Coriolis accelerations. The BREs are well-suited for capturing anisotropic coherent structures, such as streamwise streak and roll motions in boundary layers, via explicit inclusion of two short length scales associated with spatial variability in the transverse [y (cross-wind horizontal) and z (vertical)] plane and a single long length scale to capture slow streamwise development. Crucially, the parabolic nature of the BREs enables them to be marched in the streamwise direction. We perform linear stability analysis of the BREs to identify the dominant modes of instability in the convectively neutral but rotating MABL. These dominant modes are then used as inflow conditions for solving the BREs. We observe that the Coriolis accelerations support the emergence of nonlinear Ekman roll vortices that propagate across the wind, with potentially important implications for turbine power production.