Parameters for the collapse of turbulence in the stratified plane Couette flow

\u3cp\u3eWe 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.\u3c/p\u3

Shear capacity as prognostic for nocturnal boundary layer regimes

Field observations and theoretical analysis are used to investigate the appearance of different nocturnal boundary layer regimes. Recent theoretical findings predict the appearance of two different regimes: the continuously turbulent (weakly stable) boundary layer and the relatively ’quiet’ (very stable) boundary layer. A large number of nights (approx. 4500 in total) are analysed using an ensemble averaging technique. The observations support the existence of these two fundamentally different regimes: weakly stable (turbulent) nights rapidly reach a steady state (within 2-3 hours). In contrast, very stable nights reach a steady state much later after a transition period (2-6 hours). During this period turbulence is weak and non-stationary. To characterise the regime a new parameter is introduced: the Shear Capacity. This parameter compares the actual shear after sunset with the minimum shear needed to sustain continuous turbulence. In turn, the minimum shear is dictated by the heat flux demand at the surface (net radiative cooling), so that the Shear Capacity combines flow information with knowledge on the boundary condition. It is shown that the Shear Capacity enables prediction of the flow regimes. The prognostic strength of this non-dimensional parameter appears to outperform the traditional ones like z/L and Ri as regime indicator

Local characteristics of the nocturnal boundary layer in response to external pressure forcing

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 speed are formed. In this manner, the mean dynamical behavior of near-surface turbulent characteristics, and composite profiles of wind and temperature are systematically investigated. We find that the classification results 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

Near-surface temperature inversion growth rate during the onset of the stable boundary layer

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 gain more 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 (Dome C and Karlsruhe). 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