The Analysis of Turbulence Intensity and Reynolds Shear Stress in Wall-Bounded Turbulent Flows at High Reynolds Numbers

We investigated the turbulent intensities and Reynolds shear stress at high Reynolds number $({Re_\tau = 5 \times 10^{6}})$ in the atmosphere surface layer (ASL) through analyzing observations in near-neutral stratified conditions. The results show that with increasing Reynolds number the streamwise turbulent intensity increases linearly, and the peak of the Reynolds shear stress extends to a higher non-dimensional height, which means that the thickness of the logarithmic region increases. Furthermore, our results provide evidence for treating the ASL as a canonical turbulent boundary layer, the results of which can be extended and applied to higher Reynolds number wall turbulence in the ASL.     

On extension of Malkus' theory of turbulence to stably stratified shear flow

Malkus' theory of turbulent shear flow and turbulent convection is extended to stably stratified shear flow. The local Richardson number is found to be close to its critical value throughout the turbulent flow. Assuming a strong interaction between velocity and density fields requires that their profiles depend linearly on height. From this, for stratified shear flow at sufficiently high Reynolds numbers, a combination of logarithmic and linear profiles is expected. The purely linear and the log-linear profile are both observed in laboratory channel flow and in atmospheric boundary layer flow.Work undertaken while at the Department of Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.     

Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory

A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers, \({Re_{\tau}\sim\mathcal{O}(10^6)}\) . It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.     

Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.     

Stratified flow over non-uniform surfaces: Turbulent energy model

A turbulent energy model is developed to simulate the response of a neutrally stratified atmospheric boundary layer to sudden changes in surface roughness. A mechanism of turbulent energy transfer is proposed, based upon the results of numerical experiments, that explains the distribution of shear stress and hence the distribution of velocity profiles in the atmospheric surface layer. Two length scales associated with the turbulent energy equation are obtained from experimental data and the law of the wall. Turbulent energy is also predicted.The predicted growth of the internal boundary layer is slower than that obtained from mixing-length models. Also, the predicted surface shear stress obtained from the turbulent energy model is in better agreement with field data than that obtained from mixing-length models.     

Eddy exchange coefficients in numerical models of the planetary boundary layer

Specification of the eddy exchange coefficients is perhaps one of the most difficult problems in the numerical modeling of the planetary boundary layer. These coefficients have been computed from finite-difference analogs to analytical expressions associated with surface boundary-layer similarity theory, which is based on observations in an equilibrium surface layer. This procedure leads to erroneous results in the region above the surface layer and in a non-equilibrium surface layer. In addition, differencing problems arise in regions of small vertical wind shear. A new turbulence transport model has been obtained through the closure procedures for the transport equations of the Reynolds stress and the turbulent length scale. The new approach could be used to calculate Reynolds stresses and eddy exchange coefficients throughout a non-neutral planetary boundary layer under non-equilibrium conditions.     

Theory And Measurements For Turbulence Spectra And Variances In The Atmospheric Neutral Surface Layer

Predictions from a new theory for high Reynolds number turbulent boundary layers during near-neutral conditions are shown to agree well with measurements of atmospheric surface-layer variances and spectra. The theory suggests surface-layer turbulence is determined by detached eddies that largely originate in the shearing motion immediately above the surface layer; as they descend into this layer, they are strongly distorted by the local shear and impinge onto the surface. Because the origin of these eddies is non-local, they are similar to those described in previous studies as `inactive' turbulence. However, they are, in fact, dynamically highly active, supplying the major mechanism for the momentum transport, including upward bursting on the time scale of the larger eddies. The vertical velocity results show that the variance and the low frequency parts of spectra increase with height in the surface layer, while in the self similar (k₁ ^-1) range the streamwise low frequency components are approximately constant with height. These large-scale longitudinal eddies extend to a length _s, which is equal to the boundary-layer height near the surface andincreases linearly to a maximum of about three times the boundary-layer height at roughly 15 m and decreases in the upper parts of the surface layer. This lower part of the surface layer, the eddy surface layer, is the region in which the eddies impinging from layers above are strongly distorted. This new result for the atmospheric boundary layer has practical application for calculating fluctuating wind loads on structures and lateral dispersion of pollution from local sources.     

A Case Study of Turbulence in the Nocturnal Boundary Layer During the Indian Summer Monsoon

Observations from the Cloud-Aerosol Interaction and Precipitation Enhancement Experiment-Integrated Ground Observation Campaign (CAIPEEX-IGOC) provide a rare opportunity to investigate nocturnal atmospheric surface-layer processes and surface-layer turbulent characteristics associated with the low-level jet (LLJ). Here, an observational case study of the nocturnal boundary layer is presented during the peak monsoon season over Peninsular India using data collected over a single night representative of the synoptic conditions of the Indian summer monsoon. Datasets based on Doppler lidar and eddy-covariance are used for this purpose. The LLJ is found to generate nocturnal turbulence by introducing mechanical shear at higher levels within the boundary layer. Sporadic and intermittent turbulent events observed during this period are closely associated with large eddies at the scale of the height of the jet nose. Flux densities in the stable boundary layer are observed to become non-local under the influence of the LLJ. Different turbulence regimes are identified, along with transitions between turbulent periods and intermittency. Wavelet analysis is used to elucidate the presence of large-scale eddies and associated intermittency during nocturnal periods in the surface layer. Although the LLJ is a regional-scale phenomenon it has far reaching consequences with regard to surface-atmosphere exchange processes.     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Two-Point Properties Of Atmospheric Turbulence Very Close To The Ground: Comparison Of A High Resolution Les With Theoretical Models

Using the tools of large-eddy simulation (LES), rapid distortion theory andEulerian kinematic simulation, two-point properties of turbulenceare studied. It is shown how the boundary conditions in thepresent LES model are fully consistent with the new top-down understanding ofatmospheric turbulence close to the ground, wherethe turbulence is analysed in terms of turbulent eddies impinging ontothe ground, being distorted by the shear and the blocking by the wall,and experiencing the creation of an internal boundary layer within aneddy surface layer (ESL) with a height of a dozen metres.The question of very large streamwise structures is addressed, and itis shown that the k^-1 range measured in spectra for the streamwisevelocity in the ESL in several recent field experiments can be found in LES, and corresponds to streaky structures. However, thesestreaky structures are different from the low Reynolds number streaks,which induce a k^-2 range in the spectrum. Finally, two-point verticalcorrelations are studied. In particular, effects of shear and of the slope of thespectrum are analysed.     

Large-Eddy Simulation of Turbulent Flow Over a Rough Surface

A family of wall models is proposed that exhibits moresatisfactory performance than previousmodels for the large-eddy simulation (LES) of the turbulentboundary layer over a rough surface.The time and horizontally averaged statistics such asmean vertical profiles of windvelocity, Reynolds stress, turbulent intensities, turbulentkinetic energy and alsospectra are compared with wind-tunnel experimental data.The purpose of the present study is to obtain simulatedturbulent flows that are comparable with wind-tunnelmeasurements for use as the wind environment for thenumerical prediction by LES of source dispersion in theneutral atmospheric boundary layer.     

The detection and measurement of turbulent structures in the atmospheric surface layer

Turbulence data from the planetary boundary layer (PBL) indicate the presence of deterministic turbulent structures. These structures often show up as asymmetric ramp patterns in measurements of the turbulent fluctuations of a scalar quantity in the atmospheric surface layer (ASL). The sign of the slope of the sharp upstream edge of such a triangular pattern depends on the thermal stability conditions of the ASL.The turbulent structures in the ASL have been tracked by a detection method which searches for rapid and strong fluctuations in a signal — the VITA (variable interval time averaging) technique. This detection method has previously been employed in laboratory boundary layers. The VITA detection method performs well in the ASL and reveals the presence of vertically coherent turbulent structures, which look similar to those in laboratory shear flows. At the moment that a sharp temperature interface appears, the horizontal alongwind velocity shows a sharp increase, along with a sudden decrease of vertical velocity, independent of the thermal stability conditions of the ASL. The fluctuating static pressure reveals a maximum at that moment. The vertical turbulent transports show a twin-peak character around the time that the sharp jumps in the temperature and the velocity signals appear.     

Resolved-scale turbulence in the atmospheric surface layer from a large eddy simulation

Large eddy simulation has encountered difficulties in handling turbulence in the atmospheric surface layer due to deficiencies in sub-grid scale models. This paper addresses the possibility of resolving the turbulence in the upper part of the surface layer by a low-aspect ratio of grid spacing. Results show that resolved-scale shear stresses dominate over the sub-grid scale components so that effects due to the sub-grid scale model can be ignored in this region. The effects of the lower boundary condition on the resolved-scale turbulence in the upper part of the surface layer are discussed. It is concluded that the normalized mean velocity shear and resolved turbulence in the upper part of the surface layer are not affected by the specification of the lower boundary condition. In addition, the present work proposes a new independent model parameter, the Smagorinsky Reynolds Number (Re_SM), and demonstrates that this number determines the resolved turbulence in the upper part of the surface layer.     

二阶闭合模式在污染气象学中的某些应用

本文采用二阶闭合的湍流边界层模式,进行一系列数值试验以模拟边界层中连续线源的扩散状况。试验表明:无论在稳定的或不稳定的边界层中,高源的扩散能力都低于低源;在稳定层中,粗糙地表上的大气扩散能力高于光滑表面;在相同风速和地表净辐射情况下,粗糙表面上的大气扩散能力反而低于光滑表面;对流边界层中存在反梯度输送,因而K理论的应用受到限制。试验还表明,修正的Kazanski-Monin参数可能比Monin-Obukhov长度更能反映大气的扩散能力。     

Wind-Tunnel Experiments for Gas Dispersion in an Atmospheric Boundary Layer with Large-Scale Turbulent Motion

Large-scale turbulent motions enhancing horizontal gas spread in an atmospheric boundary layer are simulated in a wind-tunnel experiment. The large-scale turbulent motions can be generated using an active grid installed at the front of the test section in the wind tunnel, when appropriate parameters for the angular deflection and the rotation speed are chosen. The power spectra of vertical velocity fluctuations are unchanged with and without the active grid because they are strongly affected by the surface. The power spectra of both streamwise and lateral velocity fluctuations with the active grid increase in the low frequency region, and are closer to the empirical relations inferred from field observations. The large-scale turbulent motions do not affect the Reynolds shear stress, but change the balance of the processes involved. The relative contributions of ejections to sweeps are suppressed by large-scale turbulent motions, indicating that the motions behave as sweep events. The lateral gas spread is enhanced by the lateral large-scale turbulent motions generated by the active grid. The large-scale motions, however, do not affect the vertical velocity fluctuations near the surface, resulting in their having a minimal effect on the vertical gas spread. The peak concentration normalized using the root-mean-squared value of concentration fluctuation is remarkably constant over most regions of the plume irrespective of the operation of the active grid.     

Current problems in the stratocumulus-topped atmospheric boundary layer

Extended sheets of stratocumulus (Sc) in the upper part of the atmospheric boundary layer (ABL) often occur under appropriate meteorological conditions. These cloud decks are important both in climate studies and in weather forecasting. We review the current knowledge of the turbulent structure of the ABL capped by a cloud deck, in the light of recent observations and model studies. The most important physical processes determining this structure are longwave radiative cooling at cloud top, shortwave radiative wanning by absorption in the cloud, surface buoyancy flux, and wind shear in the ABL. As a result, turbulence can cause entrainment against the buoyancy jump at cloud top. In cases where only longwave radiative fluxes and surface buoyancy fluxes are important, the turbulent structure is relatively well understood. When shortwave radiative fluxes and/or wind shear are also important, the resulting turbulent structure may change considerably. A decoupling of the cloud from the sub-cloud layer or of the top of the cloud from the rest of the ABL is then regularly observed. In no cases are the details of the entrainment at cloud top understood well enough to derive a relatively simple formulation that is consistent with observations. Cloud-top entrainment instability may lead to the break-up of a cloud deck (but also to cloud deepening). The role of mesoscale circulations in determining fractional cloudiness is not yet well understood.     

Large-eddy simulation of turbulent flow above and within a forest

A large-eddy simulation has been performed of an atmospheric surface layer in which the lower third of the domain is occupied by a drag layer and heat sources to represent a forest. Subgridscale processes are treated using second-order closure techniques. Lateral boundaries are periodic, while the upper boundary is a frictionless fixed lid. Mean vertical profiles of wind velocity derived from the output are realistic in their shape and response to forest density. Similarly, vertical profiles of Reynolds stress, turbulent kinetic energy and velocity skewness match observations, at least in a qualitative sense. The limited vertical extent of the domain and the artificial upper boundary, however, cause some departures from measured turbulence profiles in real forests. Instantaneous turbulent velocity and scalar fields are presented which show some of the features obtained by tower instrumentation in the field and in wind tunnels, such as the vertical coherence of vertical velocity and the slope of structures revealed by temperature patterns.     

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as \(\beta \approx 5.7\) in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.     

Large-Eddy Simulation of Thermally Stratified Atmospheric Boundary-Layer Flow Using a Minimum Dissipation Model

A generalized form of a recently developed minimum dissipation model for subfilter turbulent fluxes is proposed and implemented in the simulation of thermally stratified atmospheric boundary-layer flows. Compared with the original model, the generalized model includes the contribution of buoyant forces, in addition to shear, to the production or suppression of turbulence, with a number of desirable practical and theoretical properties. Specifically, the model has a low computational complexity, appropriately switches off in laminar and transitional flows, does not require any ad hoc shear and stability corrections, and is consistent with theoretical subfilter turbulent fluxes. The simulation results show remarkable agreement with well-established empirical correlations, theoretical predictions, and field observations in the atmosphere. In addition, the results show very little sensitivity to the grid resolution, demonstrating the robustness of the model in the simulation of the atmospheric boundary layer, even with relatively coarse resolutions.     

The influence of convergence movement on turbulent transportation in the atmospheric boundary layer

Classical turbulent K closure theory of the atmospheric boundary layer assumes that the vertical turbulent transport flux of any macroscopic quantity is equivalent to that quantity‘s vertical gradient transport flux. But a cross coupling between the thermodynamic processes and the dynamic processes in the atmospheric system is demonstrated based on the Curier-Prigogine principle of cross coupling of linear thermodynamics. The vertical turbulent transportation of energy and substance in the atmospheric boundary layer is related not only to their macroscopic gradient but also to the convergence and the di-vergence movement. The transportation of the convergence or divergence movement is important for the atmospheric boundary layer of the heterogeneous underlying surface and the convection boundary layer.Based on this, the turbulent transportation in the atmospheric boundary layer, the energy budget of the heterogeneous underlying surface and the convection boundary layer, and the boundary layer parameteri-zation of land surface processes over the heterogeneous underlying surface are studied. This research offers clues not only for establishing the atmospheric boundary layer theory about the heterogeneous underlying surface, but also for overcoming the difficulties encountered recently in the application of the atmospheric boundary layer theory.