Large-Eddy Simulation of Katabatic Flows

A large-eddy simulation model with rotated coordinates and an open boundary is used to simulate the characteristics of katabatic flows over simple terrain. Experiments examine the effects of cross winds on the development of the slope-flow boundary layer for a steep (20°) slope and the role of drainage winds in preventing turbulence collapse on a gentle slope (1°). For the steep flow cases, comparisons between model average boundary-layer velocity, temperature deficit, and turbulence kinetic energy budget terms and tower observations show reasonable agreement. Results for different cross slope winds show that as the cross slope winds increase, the slope flow deepens faster and behaves more like a weakly stratified, sheared boundary layer. Analysis of the momentum budget shows that near the surface the flow is maintained by a balance between downslope buoyancy forcing and vertical turbulence flux from surface drag. Above the downslope jet, the turbulence vertical momentum flux reverses sign and acceleration of the flow by buoyancy is controlled by horizontal advection of slower moving ambient air. The turbulence budget is dominated by a balance between shear production and eddy dissipation, however, buoyancy and pressure transport both are significant in reducing the strength of turbulence above the jet. Results from the gentle slope case show that even a slight terrain variation can lead to significant drainage winds. Comparison of the gentle slope case with a flat terrain simulation indicates that drainage winds can effectively prevent the formation of very stable boundary layers, at least near the top of sloping terrain.     

Vertical Structure Of Turbulence In Offshore Flow During Rasex

The adjustment of the boundary layer immediately downstream froma coastline is examined based on two levels of eddy correlation data collected on a mast at the shore and six levels of eddy correlation data and profiles of mean variables collected from a mast 2 km offshore during the Risø Air-Sea Experiment. The characteristics of offshore flow are studied in terms of case studies and inter-variable relationships for the entire one-month data set. A turbulent kinetic energy budget is constructed for each case study.The buoyancy generation of turbulence is small compared to shear generation and dissipation. However, weakly stable and weakly unstable cases exhibit completely different vertical structure. With flow of warm air from land over cooler water, modest buoyancy destruction of turbulence and reduced shear generation of turbulence over the less rough sea surface cause the turbulence to rapidly weaken downstream from the coast. The reduction of downward mixing of momentum by the stratification leads to smaller roughness lengths compared to the unstable case. Shear generation at higher levels and advection of stronger turbulence from land often lead to an increase of stress and turbulence energy with height and downward transport of turbulence energy toward the surface.With flow of cool air over a warmer sea surface, a convective internal boundary layer develops downstream from the coast. An overlying relatively thick layer of downward buoyancy flux (virtual temperature flux) is sometimes maintained by shear generation in the accelerating offshore flow.     

大气边界层阵风相干结构的产生条件

壁湍流相干结构的发现是近代湍流研究的重大进展之一,从20世纪50年代开始,在大气边界层湍流中也发现了相干结构——对流云街,并进行了系统的研究。近些年来,人们发现在近地层湍流中也存在相干结构。利用北京325 m气象塔对城市下垫面中大风和小风天气的风速分析,发现较有规律的周期3~6 min的阵风,且有明显的相干结构,而对不同下垫面的阵风研究,均发现存在这种相干结构,这种阵风相干结构对通量输送有不可忽视的作用。本文利用2012年4月甘肃省民勤县巴丹吉林沙漠观测塔的超声风速和平均场风速、温度观测资料,对阵风相干结构的产生条件进行了分析。采用傅立叶变换,将三维超声风速按频率分成基流(周期10分钟以上)、阵风扰动(周期1到10分钟)、湍流脉动(周期小于1分钟)三部分,结合平均场的资料分析发现:阵风相干结构出现在静力中性、不稳定甚至略微稳定的条件下,或者说机械作用主导的大气边界层,阵风区就会出现相干结构,热力作用对其有抑制和干扰的作用。从而,阵风的相干结构和壁面相干结构都出现在中性条件下,是机械湍流的现象,都主导着动量能量的输运。阵风区的相干结构并不等同于对流云街,他们出现在不同的大气稳定度条件下且尺度不同。     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是，组织化对流具有边界层尺度的垂直相干性，可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合，探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料，通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法，分离组织化对流和背景湍涡，计算与两者相关的非局地和局地动量通量，发现与组织化对流相关的非局地动量通量是总通量的重要组成部分，并主导混合层中的垂直动量输送。而后，基于协谱和相位谱分析，探究组织化对流的空间结构对动量传输的影响，发现在热力主导的不稳定环境中，单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中，滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小，从而提升动量传输效率。研究结果表明，边界层方案需要包含非局地动量通量项，其参数化应考虑整体稳定度对传输效率的影响。     

Combining Non-local Scalings with a TKE Closure for Mixing in Boundary-layer Clouds

A new approach to the parametrization of the cumulus-capped boundary layer is described. It combines a traditional higher-order turbulence closure, appropriate for boundary layers where the skewness of thermodynamic variable probability distributions is low (typically stratocumulus-capped), with non-local scaled similarity functions. These are introduced in order to represent explicitly that part of the distribution arising from skewed cumulus elements and the scalings are found to work very well against equilibrium shallow cumulus large-eddy simulations. Results from a wide range of single column model simulations, from stratocumulus to shallow cumulus to cumulus rising into stratocumulus, are presented that demonstrate the validity of the approach as a means of parametrizing the cloudy boundary layer. Sensitivity tests show that enhancement of the turbulence length scales and the buoyancy production of TKE are especially important.     

Observation of a Self-Limiting,Shear-Induced Turbulent Inversion Layer Above Marine Stratocumulus

High-resolution measurements of thermodynamic, microphysical, and turbulence properties inside a turbulent inversion layer above a marine stratocumulus cloud layer are presented. The measurements are performed with the helicopter-towed measurement payload Airborne Cloud Turbulence Observation System (ACTOS), which allows for sampling with low true air speeds and steep profiles through cloud top. Vertical profiles show that the turbulent inversion layer consists of clear air above the cloud top, with nearly linear profiles of potential temperature, horizontal wind speed, absolute humidity, and concentration of interstitial aerosol. The layer is turbulent, with an energy dissipation rate nearly the same as that in the lower cloud, suggesting that the two are actively coupled, but with significant anisotropic turbulence at the large scales within the turbulent inversion layer. The turbulent inversion layer is traversed six times and the layer thickness is observed to vary between 37 and 85 m, whereas the potential temperature and horizontal wind speed differences at the top and bottom of the layer remain essentially constant. The Richardson number therefore increases with increasing layer thickness, from approximately 0.2 to 0.7, suggesting that the layer develops to the point where shear production of turbulence is sufficiently weak to be balanced by buoyancy suppression. This picture is consistent with prior numerical simulations of the evolution of turbulence in localized stratified shear layers. It is observed that the large eddy scale is suppressed by buoyancy and is on the order of the Ozmidov scale, much less than the thickness of the turbulent inversion layer, such that direct mixing between the cloud top and the free troposphere is inhibited, and the entrainment velocity tends to decrease with increasing turbulent inversion-layer thickness. Qualitatively, the turbulent inversion layer likely grows through nibbling rather than engulfment.     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

Marginal mixing theories

Abstract

Mixing near the sloping boundaries of oceans or lakes may be a significant mechanism of diapycnal transport. The basic physics of this is reviewed, with emphasis on the reduction of the effectiveness of the process due to both reduced stratification and the restratifying secondary circulation driven by buoyancy forces. This re stratification is shown to reduce the effectiveness of intermittent mixing events as well as steady mixing. It is argued that for boundary mixing to be effective in the abyssal ocean it must extend sufficiently far from the boundary that the stratification can be maintained; this may be true for breaking bottom‐reflected internal waves. The alongslope flow implied by steady‐state boundary mixing theories is downwelling‐favourable and has a magnitude related to the thickness and other properties of the boundary layer. Mixing near a boundary may thus tend to drive a downwelling‐favourable mean circulation in the interior. If the interior circulation is imposed by other forces, the bottom boundary layer may evolve to a steady state if the interior flow is downwelling‐favourable, but if it is upwelling‐favourable initially a steady state seems unlikely and the downwelling‐favourable alongslope flow induced by the boundary mixing will tend to diffuse slowly into the interior. The nature of the solution in all these cases is sensitive to the Burger number, N² sin² θ/f², where θ is the bottom slope, and to the eddy Prandtl number.     

青藏高原东北边坡复杂地形重力波的数值模拟

基于2007年7月青海祁连站的野外加密探空资料,结合高分辨率的三维边界层模式,模拟研究了青藏高原东北边坡复杂地形条件下,边界层对流引起的干动力过程对该地区地形重力波产生及传播的影响机理。结果表明:在不同的背景场强迫下,高原东北边坡复杂地形上空对流和重力波的空间结构存在较大差异。当背景风向与山体垂直时,随着风速增加,山脊背风坡混合层顶附近大气不稳定能量加强,激发了下游区域较强的重力波信号,此时对流线组织性增强、重力波波列较长,高水汽含量的空气被波峰传输到较高的高度,为对流云发展提供了有利条件;当背景风向与山脊走向平行时,山顶上空对流发展旺盛,山脊背风坡混合层顶大气状态较稳定,激发的地形重力波信号较弱且波列较短,整个混合层顶附近水汽较少,对流云形成条件减弱;当背景大气浮力频率减小时,整个区域上空对流发展更加旺盛但组织性减弱,背风坡下游重力波向上传输的距离减小,信号不显著,混合层顶附近水汽分布均匀且变化幅度较小,有利于层状云发展。     

Aircraft-Based Measurements Of Turbulence Structures In The Katabatic Flow Over Greenland

Turbulence structures in the katabatic flow in the stable boundary layer (SBL) over the ice sheet are studied for two case studies with high wind speeds during the aircraft-based experiment KABEG (Katabatic wind and boundary layer front experiment around Greenland) in the area of southern Greenland. The aircraft data allow the direct determination of turbulence structures in the katabatic flow. For the first time, this allows the study of the turbulence structure in the katabatic wind system over the whole boundary layer and over a horizontal scale of 80 km.The katabatic flow is associated with a low-level jet (LLJ), with maximum wind speeds up to 25 m s^-1. Turbulent kinetic energy (TKE) and the magnitude of the turbulent fluxes show a strong decrease below the LLJ. Sensible heat fluxes at the lowest level have values down to -25 W m^-2. Latent heat fluxes are small in general, but evaporation values of up to +13 W m^-2 are also measured. Turbulence spectra show a well-defined inertial subrange and a clear spectral gap around 250-m wavelength. While turbulence intensity decreases monotonously with height above the LLJ for the upper part of the slope, high spectral intensities are also present at upper levels close to the ice edge. Normalized fluxes and variances generally follow power-law profiles in the SBL.Terms of the TKE budget are computed from the aircraft data. The TKE destruction by the negative buoyancy is found to be very small, and the dissipation rate exceeds the dynamical production.     

Wave-Modified Flux and Plume Dispersion in the Stable Boundary Layer

The effects of a pressure jump and a following internal gravity wave on turbulence and plume diffusion in the stable planetary boundary layer are examined. The pressure jump was accompanied by a sudden increase in turbulence and plume dispersion. The effects of wave perturbations on turbulence statistics are analysed by calculating fluxes and variances with and without the wave signal for averaging times ranging from 1 to 30 min. The wave signals are obtained using a band-pass filter. It is shown that second-order turbulence quantities calculated without first subtracting the wave perturbations from the time are greater than those calculated when the wave signal is separated from the turbulence. Estimates of the vertical dispersion of an elevated tracer plume in the stable boundary layer are made using an elastic backscatter lidar. Plume dispersion observed 25 m downwind of the source increases rapidly with the arrival of the flow disturbances. Measured plume dispersion and plume centreline height correlate with the standard deviation of the vertical velocity but not with the wave signal.     

Numerical Modelling of Katabatic Flow Over a Melting Outflow Glacier

A realistic simulation of katabatic flows is not a straightforward task for numerical models. One complicating factor is that katabatic flows develop within a stably stratified boundary layer, which is poorly resolved and described in many numerical models. To capture the jet-shaped shallow flow a model set-up with high vertical resolution is also required. In this study, ‘a state of the art’ mesoscale numerical model is applied in a simulation of katabatic flow over a melting glacier. A basic agreement between observations and model results is found. From scale analysis, it is concluded that the simulated flow can be classified as katabatic. Although the background flow varies in strength and direction, the simulated katabatic flow over Breidamerkurjökull is persistent. Two factors vital for this persistence are identified. First, the melting snow maintains the surface temperature close to 0 °C while the air temperature warms adiabatically as it descends the slope. This provides a ‘self enhanced’ negative buoyancy that drives the flow to a balance with local friction. Second, the jet-like shape of the resulting flow gives rise to a large ‘curvature term’ in the Scorer parameter, which becomes negative in the upper jet. This prevents vertical wave propagation and isolates the katabatic layer of the influence from the free troposphere aloft. Our results suggest that the formation of local microclimates dominated by katabatic flow is a general feature over melting glaciers. The modelled turbulence structure illustrates the importance of non-local processes. Neglecting the vertical transport of turbulence in katabatic flows is not a valid assumption. It is also found that the local friction velocity remains larger than zero through the katabatic jet, due to directional shear where the scalar wind speed approaches its maximum.     

A wind tunnel study of air flow in waving wheat: Single-point velocity statistics

We analyse single-point velocity statistics obtained in a wind tunnel within and above a model of a waving wheat crop, consisting of nylon stalks 47 mm high and 0.25 mm wide in a square array with frontal area index 0.47. The variability of turbulence measurements in the wind tunnel is illustrated by using a set of 71 vertical traverses made in different locations, all in the horizontally-homogeneous (above-canopy) part of the boundary layer. Ensemble-averaged profiles of the statistical moments up to the fourth order and profiles of Eulerian length scales are presented and discussed. They are consistent with other similar experiments and reveal the existence of large-scale turbulent coherent structures in the flow. The drag coefficient in this canopy as well as in other reported experiments is shown to exhibit a characteristic height-dependency, for which we propose an interpretation. The velocity spectra are analysed in detail; within and just above the canopy, a scaling based on fixed length and velocity scales (canopy height and mean horizontal wind speed at canopy top) is proposed. Examination of the turbulent kinetic energy and shear stress budgets confirms the role of turbulent transport in the region around the canopy top, and indicates that pressure transport may be significant in both cases. The results obtained here show that near the top of the canopy, the turbulence properties are more reminiscent of a plane mixing layer than a wall boundary layer.     

Spectra and Cospectra of Turbulence in an Internal Boundary Layer over a Heterogeneously Irrigated Cotton Field

During the Energy Balance Experiment, patch-to-patch irrigation generated gradients in soil moisture in a north-south oriented cotton field. An internal boundary layer (IBL) developed as a result of strong horizontal advection from relatively dry upstream patches to relatively wet downstream patches associated with the prevailing northerly winds. This generated large eddies of multiple sizes, which had significant influences on the structure of turbulence in the IBL. The power spectra and cospectra of wind speed, temperature, humidity, and energy fluxes measured at two heights within the IBL are presented and used to investigate the influence of the IBL on surface layer turbulence. The spectra and cospectra were greatly enhanced by external disturbances at low frequencies. The peak frequencies of these disturbances did not change with height. The spectra and cospectra typically converged and were parallel to the Kansas spectrum at high frequencies (in the inertial subrange). A clear gap in the spectra of horizontal wind velocity existed at intermediate frequencies when the surface layer was stable. The results indicate that large eddies that originated in the upstream convective boundary layer had considerable impacts on the spectra and cospectra of surface layer turbulence. The influence of these large eddies was greater (1) when the IBL was well-developed in the near surface layer than when the IBL did not exist, (2) at higher levels than at lower levels, and (3) when the atmospheric surface layer (ASL) was unstable than when the ASL was stable. The length scales of these large eddies were consistent with the dominant scales of surface heterogeneity at the experiment site.     

Impact of Sea-Spray on the Atmospheric Surface Layer

The feedback effects of sea-spray on the heat and momentum fluxes under equilibrium conditions associated with winds of tropical cyclones are investigated using a one-dimensional coupled sea-spray and atmospheric surface-layer (ASL) model. This model is capable of simulating the microphysical aspects of the evaporation of saline water droplets of various sizes and their dynamic and thermal interaction with the turbulence mixing that is simulated by the Mellor–Yamada 1.5-order closure scheme. Sea-spray droplet generation is described by a state-of-the-art parametrization that predicts the size spectrum of sea-spray droplets for a given surface forcing. The results from a series of simulations indicate the way in which evaporating droplets of various sizes modify the turbulence mixing near the surface, which in turn affects further droplet evaporation. All these results are direct consequences of the effects of sea-spray on the balance of turbulent kinetic energy in the spray-filled surface layer. In particular, the overall impact of sea-spray droplets on the mean wind depends on the wind speed at the level of sea-spray generation. When the wind speed is below 40 m s⁻¹, the droplets are small in size and tend to evaporate substantially and thus cool the spray-filled layer, while for wind speeds above 50 m s⁻¹, the size of the droplets is so large that they do not have enough time to evaporate much before falling back into the sea. The sensible heat carried by the droplets is released to the ambient air, increasing the buoyancy of the surface layer and enhancing the turbulent mixing. The suspension of sea-spray droplets reduces the buoyancy and makes the surface layer more stable, decreasing the friction velocity and the downward turbulent mixing of momentum. The results from the numerical experiments also suggest that, in order not to violate the constant flux assumption critical to the Monin–Obukhov similarity theory, a displacement equal to the mean wave height should be included in the logarithmic profiles of the wind and thermal fields.     

Turbulence in the Stable Boundary Layer at Higher Richardson Numbers

We present some algebraic and numerical simulations of the stable boundary layer. We also discuss the problem of the existence of a critical Richardson number (Ri), beyond which the turbulence is suppressed. We compare the results of a second-order algebraic model with those of a third-order numerical model and, to this purpose, numerical simulations of a wind-tunnel flow, which is characterized by various Richardson numbers, were performed. As far as the second-order model is concerned, solutions, for the Richardson number greater than any critical value, can be obtained by modifying the time scales of the second-order equation pressure correlation terms in order to account for a buoyancy damping factor. We show that using a third-order model allows the same results (no critical Richardson number) to be obtained without modifications to the time scales. It is suggested that the non-locality, accounted for by the third-order moments, could allow the turbulence to persist also for Ri > 1.     

Temporal Oscillations in the Convective Boundary Layer Forced by Mesoscale Surface Heat-Flux Variations

A theoretical approach suggests that the surface heterogeneity on a scale of tens of kilometres can generate mesoscale motions that are not in a quasi-stationary state. The starting point of the theoretical approach is the equations of horizontal velocity and potential temperature that are low-pass filtered with a mesoscale cut-off wavelength. The transition of the generated mesoscale motions from a quasi-stationary state to a non-stationary state occurs when horizontal advection is strong enough to level out the potential temperature gradient on the surface heterogeneity scale. Large-eddy simulations (LES) suggest that the convective boundary layer (CBL) changes to a non-stationary state when forced by a surface heat-flux variation of amplitude of 100W m⁻² or higher and a wavelength of the order of 10 km. Spectral analysis of the LES reveals that when the mesoscale motions are in a quasi-stationary state, the energy provided by the surface heat-flux variation remains in organized mesoscale motions on the scale of the surface variation itself. However, in a non-stationary state, the energy cascades to smaller scales, with the cascade extending down into the turbulence scale when the wavelength of the surface heat-flux variation is on a scale smaller than 100 times the CBL height. The energy transfer from the generated mesoscale motions to the CBL turbulence results in the absence of a spectral gap between the two scales. The absence of an obvious spectral gap between the generated mesoscale motions and the turbulence raises questions about the applicability of mesoscale models for studies on the effect of high-amplitude surface heterogeneity on a scale of tens of kilometres. The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.