We perform direct numerical simulation of the Couette flow as a model for the stable boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux. First, we establish what the similarities and differences are between applying a fixed buoyancy difference (Dirichlet) and a fixed buoyancy flux (Neumann) as boundary conditions. Moreover, two distinct parameters were recently proposed for the turbulent-to-laminar transition: the Reynolds number based on the Obukhov length and the "shear capacity," a velocity-scale ratio based on the buoyancy flux maximum. We study how these parameters relate to each other and to the atmospheric boundary layer. The results show that in a weakly stratified equilibrium state, the flow statistics are virtually the same between the different types of boundary conditions. However, at stronger stratification and, more generally, in nonequilibrium conditions, the flow statistics do depend on the type of boundary condition imposed. In the case of Neumann boundary conditions, a clear sensitivity to the initial stratification strength is observed because of the existence of multiple equilibriums, while for Dirichlet boundary conditions, only one statistically steady turbulent equilibrium exists for a particular set of boundary conditions. As in previous studies, we find that when the imposed surface flux is larger than the maximum buoyancy flux, no turbulent steady state occurs. Analytical investigation and simulation data indicate that this maximum buoyancy flux converges for increasing Reynolds numbers, which suggests a possible extrapolation to the atmospheric case.@en

Investigation of meteorological measurements along a 45 m tower at Dome C on the high East Antarctic Plateau revealed two distinct stable boundary layer (SBL) regimes at this location. The first regime is characterized by strong winds and continuous turbulence. It results in full vertical coupling of temperature, wind magnitude and wind direction in the SBL. The second regime is characterized by weak winds, associated with weak turbulent activity and very strong temperature inversions reaching up to 25 K in the lowest 10 m. Vertical temperature profiles are generally exponentially shaped (convex) in the first regime and ‘convex–concave–convex’ in the second. The transition between the two regimes is particularly abrupt when looking at the near-surface temperature inversion and it can be identified by a 10 m wind-speed threshold. With winds under this threshold, the turbulent heat supply toward the surface becomes significantly lower than the net surface radiative cooling. The threshold value (including its range of uncertainty) appears to agree with recent theoretical predictions from the so-called ‘minimum wind speed for sustainable turbulence’ (MWST) theory. For the quasi-steady, clear-sky winter cases, the relation between the near-surface inversion amplitude and the wind speed takes a characteristic ‘S’ shape. Closer analysis suggests that this relation corresponds to a ‘critical transition’ between a steady turbulent and a steady ‘radiative’ regime, with a dynamically unstable branch in the transition zone. These fascinating characteristics of the Antarctic boundary layer challenge present and future numerical models to represent this region in a physically correct manner.

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A conceptual model is used in combination with observational analysis to understand regime transitions of near-surface temperature inversions at night as well as in Arctic conditions. The model combines a surface energy budget with a bulk parameterization for turbulent heat transport. Energy fluxes or feedbacks due to soil and radiative heat transfer are accounted for by a "lumped parameter closure," which represents the "coupling strength" of the system. Observations from Cabauw, Netherlands, and Dome C, Antarctica, are analyzed. As expected, inversions are weak for strong winds, whereas large inversions are found under weak-wind conditions. However, a sharp transition is found between those regimes, as it occurs within a narrow wind range. This results in a typical S-shaped dependency. The conceptual model explains why this characteristic must be a robust feature. Differences between the Cabauw and Dome C cases are explained from differences in coupling strength (being weaker in the Antarctic). For comparison, a realistic column model is run. As findings are similar to the simple model and the observational analysis, it suggests generality of the results. Theoretical analysis reveals that, in the transition zone near the critical wind speed, the response time of the system to perturbations becomes large. As resilience to perturbations becomes weaker, it may explain why, within this wind regime, an increase of scatter is found. Finally, the so-called heat flux duality paradox is analyzed. It is explained why numerical simulations with prescribed surface fluxes show a dynamical response different from more realistic surface-coupled systems.

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The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin–Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. In addition, it is shown that the idealized, nocturnal boundary-layer system shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.

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Geostrophic wind speed data, derived from pressure observations, are used in combination with tower measurements to investigate the nocturnal stable boundary layer at Cabauw, the Netherlands. Since the geostrophic wind speed is not directly influenced by local nocturnal stability, it may be regarded as an external forcing parameter of the nocturnal stable boundary layer. This is in contrast to local parameters such as in situ wind speed, the Monin-Obukhov stability parameter (z/L), or the local Richardson number. To characterize the stable boundary layer, ensemble averages of clear-sky nights with similar geostrophic wind speeds are formed. In this manner, the mean dynamical behavior of near-surface turbulent characteristics and composite profiles of wind and temperature are systematically investigated. The classification is found to result in a gradual ordering of the diagnosed variables in terms of the geostrophic wind speed. In an ensemble sense the transition from the weakly stable to very stable boundary layer is more gradual than expected. Interestingly, for very weak geostrophic winds, turbulent activity is found to be negligibly small while the resulting boundary cooling stays finite. Realistic numerical simulations for those cases should therefore have a comprehensive description of other thermodynamic processes such as soil heat conduction and radiative transfer.

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This study aims to find the typical growth rate of the temperature inversion during the onset of the stable boundary layer around sunset.The sunset transition is a very challenging period for numerical weather prediction, since neither accepted theories for the convective boundary layer nor those for the stable boundary layer appear to be applicable. To gainmore insight in this period, a systematic investigation of the temperature inversion growth rate is conducted. A statistical procedure is used to analyze almost 16 years of observations from the Cabauw observational tower, supported by observations from two additional sites (DomeCandKarlsruhe). The results show that, on average, the growth rate of the temperature inversion (normalized by the maximum inversion during the night) weakly declines with increasing wind speed. The observed growth rate is quantitatively consistent among the sites, and it appears insensitive to various other parameters. The results were also insensitive to the afternoon decay rate of the net radiation except when this decay rate was very weak. These observations are compared to numerical solutions of three models with increasing complexity: a bulk model, an idealized single-column model (SCM), and an operational-level SCM. It appears only the latter could reproduce qualitative features of the observations using a first-order closure. Moreover, replacing this closure with a prognostic TKE scheme substantially improved the quantitative performance. This suggests that idealized models assuming instantaneous equilibrium flux-profile relations may not aid in understanding this period, since history effects may qualitatively affect the dynamics.

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