van de Bjh Bas Wiel

A conceptual view on inertial oscillations and nocturnal low-level jets

In the present work Blackadar’s concept of nocturnal inertial oscillations is extended. Blackadar’s concept describes frictionless inertial oscillations above the nocturnal inversion layer. The current work includes frictional effects within the nocturnal boundary layer. It is shown that the nocturnal wind speed profile describes an oscillation around the nocturnal equilibrium wind vector, rather than around the geostrophic wind vector (as in the Blackadar case). By using this perspective, continuous time-dependent wind profiles are predicted. As such, information on both the height and the magnitude of the nocturnal low-level jet is available as a function of time. Preliminary analysis shows that the proposed extension performs well in comparison with observations when a simple Ekman model is used to represent the equilibrium state in combination with a realistic initial velocity profile. In addition to jet dynamics, backward inertial oscillations are predicted at lower levels close to the surface, which also appear to be present in observations. The backward oscillation forms an important mechanism behind weakening low-level winds during the afternoon transition. Both observational and theoretical modeling studies are needed to explore this phenomenon further.

The Minimum Wind Speed for Sustainable Turbulence in the Nocturnal Boundary Layer

The collapse of turbulence in the nocturnal boundary layer is studied by means of a simple bulk model that describes the basic physical interactions in the surface energy balance. It is shown that for a given mechanical forcing, the amount of turbulent heat that can be transported downward is limited to a certain maximum. In the case of weak winds and clear skies, this maximum can be significantly smaller than the net radiative loss minus soil heat transport. In the case when the surface has low heat capacity, this imbalance generates rapid surface cooling that further suppresses the turbulent heat transport, so that eventually turbulence largely ceases (positive feedback mechanism). The model predicts the minimum wind speed for sustainable turbulence for the so-called crossing level. At this level, some decameters above the surface, the wind is relatively stationary compared to lower and higher levels. The critical speed is predicted in the range of about 5–7 m s21, depending on radiative forcing and surface properties, and is in agreement with observations at Cabauw. The critical value appears not very sensitive to model details or to the exact values of the input parameters. Finally, results are interpreted in terms of external forcings, such as geostrophic wind. As it is generally larger than the speed at crossing height, a 5 m s21 geostrophic wind may be considered as the typical limit below which sustainable, continuous turbulence under clear-sky conditions is unlikely to exist. Below this threshold emergence of the very stable nocturnal boundary layer is anticipated.

The Cessation of Continuous Turbulence as Precursor of the Very Stable Nocturnal Boundary Layer

The mechanism behind the collapse of turbulence in the evening as a precursor to the onset of the very stable boundary layer is investigated. To this end a cooled, pressure-driven flow is investigated by means of a local similarity model. Simulations reveal a temporary collapse of turbulence whenever the surface heat extraction, expressed in its nondimensional form h/L, exceeds a critical value. As any temporary reduction of turbulent friction is followed by flow acceleration, the long-term state is unconditionally turbulent. In contrast, the temporary cessation of turbulence, which may actually last for several hours in the nocturnal boundary layer, can be understood from the fact that the time scale for boundary layer diffusion is much smaller than the time scale for flow acceleration. This limits the available momentum that can be used for downward heat transport. In case the surface heat extraction exceeds the so-called maximum sustainable heat flux (MSHF), the near-surface inversion rapidly increases. Finally, turbulent activity is largely suppressed by the intense density stratification that supports the emergence of a different, calmer boundary layer regime.

Early Warning Signals for Regime Transition in the Stable Boundary Layer: A Model Study

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.

Comments on “An extremum solution of the Monin-Obukhov similarity equations"

Recently, Wang and Bras (2010, hereafter WB10)postulated an extremum hypothesis (EH) of turbulenttransportintheatmosphericsurfacelayer(ASL).Basedon this hypothesis, they derived a unique solution of thewell-knownMonin–Obukhovsimilaritytheory(MOST)equations.Throughoutthepaper,WB10highlightedthesignificance of EH and associated results. We summa-rize a few of their claims below (mostly in the authors’own words):

Predicting Nocturnal Wind and Temperature Profiles Based on External Forcing Parameters

We introduce a simple, physically consistent method to predict nocturnal wind and temperature profiles from external forcing parameters such as the geostrophic wind. As an indicator of the radiative ‘forcing’ the net longwave radiative cooling is used as a proxy. Surface fluxes are expressed in terms of these parameters by coupling an Ekman model to a rudimentary surface energy balance. Additionally the model assumes validity of Monin-Obukhov similarity in order to predict near-surface wind and temperature profiles up to a height equal to the Obukhov length. The predictions are validated against an independent dataset that covers 11-years of observations at Cabauw, The Netherlands. It is shown that the characteristic profiles in response to external forcings are well-captured by the conceptual model. For this period the observational climatology is in close agreement with ECMWF re-analysis data. As such, the conceptual model provides an alternative tool to giving a first-order estimate of the nocturnal wind and temperature profile near the surface in cases when advanced numerical or observational infrastructure is not available.

The collapse of turbulence in the atmospheric boundary layer

A well-known phenomenon in the atmospheric boundary layer is the fact that winds may become very weak in the evening after a clear sunny day. In these quiet conditions usually hardly any turbulence is present. Consequently this type of boundary layer is referred to as the quasi-laminar boundary layer. In spite of its relevance, the appearance of laminar boundary layers is poorly understood and forms a long standing problem in meteorological research. Here we investigate an analogue problem in the form of a stably stratified channel flow. The flow is studied with a simplified atmospheric model as well as with Direct Numerical Simulations. Both models show remarkably similar behaviour with respect to the mean variables such as temperature and wind speed. The similarity between both models opens new way for understanding and predicting the laminarization process. Mathematical analysis on the simplified model shows that relaminarization can be understood from the existence of a definite limit in the maximum sustainable heat flux under stably stratified conditions. This fascinating aspect will be elaborated in future work.

Interpolation error in DNS simulations of turbulence: consequences for particle tracking

An important aspect in numerical simulations of particle laden turbulent flows is the interpolation of the flow field. For the interpolation different approaches are used. Where some studies use low order linear interpolation others use high order spline methods. We compare several interpolation methods and conclude that interpolation based on B-spline functions has several advantages compared with traditional methods. First, B-spline interpolation can be executed very efficiently by optimal use of the pseudo spectral code, only one FFT needs to be executed where Hermite spline needs multiple FFTs for computing the derivatives. Second, the smoothness of the interpolated field is higher than that of Hermite spline interpolation. Finally, the interpolation error almost matches the one of Hermite spline which is not reached by the other methods investigated. Further, we focus on estimating the interpolation error and compare it with the discretisation error of the flow field. In this way one can balance the errors in order to achieve an optimal result. Algorithms have been developed for the approximation of the interpolation error. As a spin-off of the theoretical analysis a practical method is proposed which enables direct estimation of the interpolation error from the energy spectrum, which may provide a quantitative indicator for this purpose.