Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model

Abstract

Abstract. Small-scale processes in atmospheric boundary layers are typically not resolved due to cost constraints but modeled based on physical relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed in the present study with the aid of the one-dimensional turbulence (ODT) model. ODT is applied as stand-alone column model to numerically investigate stratification effects in long-lived transient Ekman flows as canonical example of polar boundary layers by resolving turbulent winds and fluctuating temperature profiles on all relevant scales of the flow. We first calibrate the adjustable model parameters for neutral cases based on the surface drag law which yields slightly different optimal model set-ups for finite low and moderate Reynolds numbers. For the stably stratified cases, previously calibrated parameters are kept fixed and the model predictions are compared with various reference numerical simulations and also observations by an exploitation of boundary layer similarity. ODT reasonably captures the temporally developing flow for various prescribed stratification profiles, but fails to fully capture the near-surface laminarization by remaining longer in a fully developed turbulent state, which suggests preferential applicability to high-Reynolds-number flow regimes. Nevertheless, the model suggests that large near-surface turbulence scales are primarily affected by the developing stratification due to scale-selective buoyancy damping which agrees with the literature. The variability of the wind-turning angle represented by the ensemble of stratified cases simulated covers a wider range than reference reanalysis data. The present study suggests that the vertical-column ODT formulation that is highly resolved in space and time can help to accurately represent multi-physics boundary-layer and subgrid-scale processes, offering new opportunities for analysis of very stable polar boundary layer and atmospheric chemistry applications.

Stochastic deconvolution of wall statistics in Reynolds‐averaged Navier–Stokes simulations based on one‐dimensional turbulence

“…A size‐ l eddy event is probabilistically accepted with local rate $$\tau ^{-1}=C\sqrt {2E/l^2}$$, where $$E=E_\mathrm{kin}-ZE_\mathrm{vp}$$ is the current specific available eddy energy that for incompressible shear flow only takes kinetic energy ( E kin ) and viscous ‘penalty’ energy ( E vp ) contributions. In the present application, the free ODT model parameters are fixed at $$C=6.5$$ and $$Z=300$$ (following Glawe [27]), which is a reasonable selection for low‐Reynolds number channel and boundary‐layer type flows [28–30]. For further details on the model formulation, the reader is directed to [14, 23, 31]…”

“…This might be a significant limitation of the model if such data would be crucial. This could be the detection of flow separation events, but for such cases surrogate analysis of ODT eddy events would seem more reasonable [30]. Hence, it is perhaps most important that the ODT model provides economical means to statistically evaluate the magnitude and frequency of some relevant diversions from the mean state, enabled solely by post-processing of a RaNS solution.…”