We have worked on a new benchmark simulation for neutrally stratified turbulent Ekman flow which is the physical problem studied in this problem as a surrogate of the real planetary boundary layer. This simulation sets a new standard for direct numerical simulation of such problems both in terms of accuracy and parallel efficiency of the algorithms used and in terms of domain size and scale separation reached -- the key parameter when it comes to a comparison with real-world problems. Based on these simulations, we have developed a closed formulation of the mean velocity profiles for neutrally stratified Ekman flow that appears consistent for the entire range of physically relevant Reynolds numbers.
Further, first steps were undertaken to bridge the gap between the surrogate problem (turbulent Ekman flow) and the real-world boundary layer through a Large-Eddy Simulation study of an extremely stable boundary layer. In this task, we make use of recent observations from the MOSAiC campaign where data at unseen accuracy and in an unprecedented amount from the Arctic became available. These Large-Eddy Simulations span a regime of boundary-layer flow that has not been investigated so far due to both lack of observations and lack of the ability of tools to study these regimes. We now have the observational data to guide sophisticated numerical process studies in this regime and have worked on extending an existing model set-up into this regime. This includes a combination of technical adaptations, i.e. smaller grid resolution to account for the much smaller size of turbulent vortices and shallower boundary layer, extreme surface parameters, and physical adjustments such as the consideration of radiation in a clear-sky enivronment close to the surface. This becomes relevant due to the extreme temperature gradients (15K per 10 m in vicinity of the surface) encountered in these regimes.
To eliminate another constraint that comes with our approach to the problem, we work on the consideration of surface roughness in our direct-numerical-simulation set-up. This was not anticipated originally, but appears as a major issue to overcome in stratified flows where the classical modelling approach (Monin-Obukhov Similarity theory) fails. We have implemented an immersed-boundary scheme based on interpolation using spline methods to our numerical tool-suite and tested this scheme. The next steps in this respect are a thorough validation of this novel approach in direct numerical simulation of stratified boundary layers including a staggering approach to overcome pressure-velocity decoupling issues that are encountered when the problem is forced at the smallest scales as it happens in presence of an immersed boundary characterizing small-scale mechanical heterogeneity.
