Of Direct Numerical Simulation of the Aerodynamically Rough Atmospheric Boundary Layer - Implementation of an Immersed Boundary Method for Turbulent Ekman Flow.

Direct numerical simulation (DNS) of the atmospheric boundary layer (ABL) is becoming more and more popular - along with the increasing power of high-performance computing. Nowadays, geophysically relevant domain sizes and simulation durations can be attained. To some extent, geophysical flows in nature are predominantly flows over rough surfaces, which significantly affects drag, mixing and transport properties of the flow. For such flows, a method is needed to impose solid walls while maintaining the efficient and tuned numerical methods for Cartesian meshes. This is achieved by an immersed boundary method (IBM), where three-dimensional roughness elements are fully resolved at the bottom wall of the simulation domain. The current IBM combined with compact schemes avoids the Gibbs phenomenon by preserving the homogeneity of spacial operators. However, the implementation of this IBM into the DNS algorithm poses challenges when applying the thermal boundary conditions on the roughness elements in the case of stably stratified ABL, but also with respect to potential appearance of spurious oscillations in the case of collocated grids for pressure and velocity.