Simulation of Turbulence in the Very Stable Boundary Layer

Motivation. Despite considerable efforts investigating the SBL, the correct parametrization of turbulent fluxes and a physically-based representation of turbulence in the SBL remain a challenge. This, in particular, is true under very stable stratification where turbulence is typically not in equilibrium and a variety of processes interact. Unfortunately, for such problems a study of LES has proven difficult as the concept of turbulence closures fails if the stratification is strong enough to cause local or temporal cessation of turbulence.

Tool. We pursue in this work, which follows Ansorge & Mellado (2014), a relatively new avenue to study the SBL, namely direct numerical simulation which is becoming available for geophysical problems due to the strong development of high-performance computing. While the necessity to resolve all scales relevant to the flow restricts our work to relatively small Reynolds numbers when compared to the atmosphere, it enables to study solutions of the governing equations without effects of sub-grid scale closures under well-defined and controlled conditions. In particular, we can study the flow for all Richardson numbers, i.e. at arbitrary stability; no matter if, on the one hand, the turbulence ceases (locally or globally) or, on the other hand, the neutral limit is approached. Moreover, the entire flow-resolved spatially and temporally-is potentially at our hands for analysis: a advantage over laboratory experiments and atmospheric measurements.

As simplified configuration representative of an atmospheric boundary layer we choose Ekman flow over a smooth surface. This configuration depends on two non-dimensional parameters: a Richardson number characterizing stratification and a Reynolds number characterizing the turbulence scale separation. A fully turbulent and statistically converged neutrally stratified simulation is studied as reference for three Reynolds numbers Re=500, Re=750, and Re=1000. This allows to disentangle effects of the intermediate Reynolds number from stratification effects once stratified cases are considered.

Results. For the neutrally stratified cases, we show that the analogy of the surface layer in Ekman flow with turbulent channels holds for the budget of turbulent kinetic energy, and not only for the logarithmic law of the mean velocity. This leads to a the alignment of turbulent stress and velocity shear as expected from theoretical considerations. In the outer layer of the flow, where the mean wind turns considerably, the misalignment is, however, independent of the Reynolds number and thus a fundamental feature of this flow.

Regarding stable stratification, our simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and decoupling of the surface layer from the atmosphere. We can thus recover all regimes of static stability in a turbulent and atmosphere-like setup. We demonstrate this setup's applicability to the atmospheric problem, and estimate the Monin-Obukhov stability correction for stable stratification as 5.7z/L + 1 where L is the Obukhov length and z the height above ground. in agreement with data from channel flow and atmospheric observations.

Our data allow for the quantification of turbulent kinetic energy carried by coherent motions, potentially gravity waves, in the upper part of the boundary layer. We find that this portion can be large (on the order of 50%) and that these motions are associated with potential flow-regions, that is, non-turbulent patches. Even though these coherent motions have characteristic time scales of several eddy-turnover times, they are an important contributor to mixing in the outer layer of the flow. This suggests that these motions and associated time scales should be taken into account when studying the SBL.

Global intermittency can occur without external perturbations of the flow: in our cases it is simulated despite the absence of finite-size triggers from synoptic conditions, low-level jets or surface heterogeneities. It is hence intrinsic to a stable atmospheric boundary layer beyond a certain stability limit. We also observe that global intermittency is governed by a large-scale structure in the outer layer. This suggests that global intermittency cannot be treated as an on-off process in time, but should rather be seen as happening in time and space.

Conclusions. Due to the elimination of turbulence closure schemes, in our work it becomes possible to study atmosphere-like setups under arbitrary stratification in a unified and well-controlled setup. This allows for the numerical study of turbulence regimes that have not been accessible to other turbulence-resolving tools such as LES and Reynolds-averaged methods due to issues with turbulence closures under very stable stratification. By this method, we gain new insight into the fundamental dynamics of the SBL and quantitatively study certain aspects of turbulence closures including their a priori evaluation.

References

Ansorge, C. and Mellado, J. P. (2014): Global Intermittency and Collapsing Turbulence in a Stratified Planetary Boundary Layer. Boundary-Layer Meteorology, Under Review.