Turbulence Anisotropy in the Near-Surface Atmosphere and the Evaluation of Multiple Outer Length Scales

Length scales determined by maximum turbulent kinetic energy (TKE), the integral scale, and two length scales based on Reynolds stress-tensor anisotropy are compared to the often stated outer length scales of boundary-layer depth and distance from the earth’s surface, $z$ . The scales are calculated using sonic anemometer data from two elevations, 5 and 50 m above the ground at the main tower site of the CASES-99 field campaign. In general, none of these scales agrees with the other, although the scale of maximum TKE is often similar to the boundary-layer depth during daytime hours, and the length scales derived from anisotropy characteristics are sometimes similar to $\kappa \!z, z$ , and $2z$ depending on scale definition and thermal stability. Except for the scale with the strictest isotropy threshold, the turbulence is anisotropic for each of the various candidates for the outer scale. Length scales for maximum buoyancy flux and temperature variance are evaluated and the turbulence characteristics at these scales are almost always found to be anisotropic.     

The Near-Surface Stress Profile and Conditional Averaging of Turbulence

Using the conditional average formulation, we suggest a new explanation for why the stress in the atmospheric surface layer is often observed to vary with height. In essence, because turbulence series are always correlated for small lags, the steady-state equations of motion with negligible viscous terms that traditionally require vertical fluxes to be constant with height accordingly now require the vertical fluxes to vary with height. This result has implications for interpreting and validating Monin–Obukhov similarity theory.     

The Use of Weather Forecasts to Characterise Near-Surface Optical Turbulence

The propagation of optical and electromagnetic waves is affected by small-scale atmospheric turbulence, quantified by the structure parameter of the refractive index. In the atmospheric surface layer, the mean structure parameter C_n²{C_{n}^{2}} , as averaged over the large-scale turbulence, relates to meteorological forcings through well-documented relationships. Present-day numerical weather forecast models routinely produce these forcings at the global scale. This study introduces a method where the products of such a model are used to calculate the mean optical turbulence near the surface. The method is evaluated against scintillometry measurements over climatologically distinct sites in Western Europe. The diurnal cycle modulation, and regional and seasonal contrasts, are all reproduced by our predictions. Hence, the present method explains and predicts some essential aspects of the meteorological variability of C_n²{C_{n}^{2}} near the surface. The noted discrepancies combine instrumental limitations, site peculiarities, differences related to distinct averaging procedures, and model errors, notably from weather forecasts. The minute-scale fluctuations of the measured scintillation rate are also analysed in the light of the forecast weather conditions. Fair-weather daytime periods consistently show a small short-term variability compared to the nighttime and perturbed weather periods. Thus, this short-term variability appears to have a predictable component.     

Impact of Boundary-Layer Processes on Near-Surface Turbulence Within the West African Monsoon

High frequency measurements of near-surface meteorological data acquired in north Benin during the 2006 West African monsoon seasonal cycle, in the context of the African Monsoon Multidisciplinary Analysis (AMMA) experiment, offer insight into the characteristics of surface turbulence in relation to planetary boundary-layer (PBL) processes. A wide range of conditions is encountered at the lower and upper limits of the PBL: (i) from water-stressed to well-fed vegetation, and (ii) from small to large humidity and temperature jumps at the PBL top inversion, due to the Saharan air layer overlying the monsoonal flow. As a result, buoyant convection at the surface and entrainment at the PBL top play very different roles according to the considered scalar. We show that, when the boundary-layer height reaches the shear level between the monsoonal and Harmattan flows, the temperature source and humidity sink at the boundary-layer top are sufficient to allow the entrainment to affect the entire boundary layer down to the surface. This situation occurs mainly during the drying and moistening periods of the monsoon cycle and affects the humidity statistics in particular. In this case, the humidity turbulent characteristics at the surface are no longer driven solely by buoyant convection, but also by entrainment at the boundary-layer top. Consequently, the Monin–Obukhov similarity theory appears to fail for the parameterisation of humidity-related moments.     

Microstructure of Turbulence in the Stably Stratified Boundary Layer

The microstructure of a stably stratified boundary layer, with a significant low-level nocturnal jet, is investigated based on observations from the CASES-99 campaign in Kansas, U.S.A. The reported, high-resolution vertical profiles of the temperature, wind speed, wind direction, pressure, and the turbulent dissipation rate, were collected under nocturnal conditions on October 14, 1999, using the CIRES Tethered Lifting System. Two methods for evaluating instantaneous (1-sec) background profiles are applied to the raw data. The background potential temperature is calculated using the “bubble sort” algorithm to produce a monotonically increasing potential temperature with increasing height. Other scalar quantities are smoothed using a running vertical average. The behaviour of background flow, buoyant overturns, turbulent fluctuations, and their respective histograms are presented. Ratios of the considered length scales and the Ozmidov scale are nearly constant with height, a fact that can be applied in practice for estimating instantaneous profiles of the dissipation rate.     

Measurements Of Turbulence Transfer In The Near-Surface Layer Over The Southeastern Tibetan Plateau

Turbulent flux measurements at Qamdo site over the Tibetan Plateau during TIPEX from May 18 to June 30, 1998 are presented. Sensible heat dominated,accounting for about 66% of the available energy (the sum of net radiation and soil heat flux) prior to the monsoon(dry period), reducing to about 31%, with latent heat increased to about 56% of available energy,in the monsoon season (wet period). Surface energy budget closure on average was about 0.80 (0.85)prior to the monsoon and 0.89 (0.76) during the monsoon using eddy correlation (profile) methods. The sum of latent and sensible heat fluxes calculated from the flux-profilemethod was smaller by about 15% than that from eddy correlation. Martano's method is used toestimate the surface aerodynamic roughness length z₀ and zero plane displacement d from singlelevel sonic anemometer data, giving d = 0.12 m and z₀ = 0.08 m. The overall neutral dragcoefficient (C_DN) and scalar coefficient (C_HN) were found to be C_DN = 0.0055and C_HN = 0.0059 in the southeastern area of Tibet. Their variations with the mean wind speed at 10 m are discussed.     

Comparing Estimates of Turbulence Based on Near-Surface Measurements in the Nocturnal Stable Boundary Layer

Tethered Lifting System (TLS) estimates of the dissipation rate of turbulent kinetic energy (e){(\varepsilon)} are reasonably well correlated with concurrent measurements of vertical velocity variance (s_w²){(\sigma_{w}^{2})} obtained from sonic anemometers located on a nearby 60-m tower during the CASES-99 field experiment. Additional results in the first 100 m of the nocturnal stable boundary layer confirm our earlier claim that the presence of weak but persistent background turbulence exists even during the most stable atmospheric conditions, where e{\varepsilon} can exhibit values as low as 10⁻⁷ m² s⁻³. We also present a set of empirical equations that incorporates TLS measurements of temperature, horizontal wind speed, and e{\varepsilon} to provide a proxy measurement for s_w²{\sigma_{w}^{2}} at altitudes higher than tower heights.     

Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence

One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh.Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.     

云南大理干湿季近地层湍流特征对比分析

利用大理国家气候观象台2007年3月至2008年1月观测资料,采用涡动相关法等计算方法分析了该地区湍流强度、湍流方差、湍流通量等特征量的日变化规律和干湿季变化特征。结果表明：湍流强度干季大于湿季;湍流方差与稳定度满足1／3次方定律,风速方差在稳定条件下比不稳定条件下离散,水平方向比垂直方向离散;湍流通量有明显日变化特征,感热、动量通量干季大于湿季,潜热通量湿季大于干季,干湿季热量交换以潜热为主。     

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.     

Steps, Waves and Turbulence in the Stably Stratified Planetary Boundary Layer

The stably-stratified planetary boundary layer contains small-vertical-scale, step-like structures, waves on a multitude of scales, large horizontal eddies and small-scale turbulence, all of which constantly interact with, and modify, one another. Current knowledge of how the various components act in the vicinity of the step-like structures is surveyed. It is concluded that packets of internal waves are the main conduit for interaction within and across the boundary layer, and low-intensity critical-level absorption at the fringes of their spectrum probably maintains the step-like structures. Further investigation of the processes requires intensive observations of the four-dimensional structure of the region, but such an investigation will need a new generation of high-resolution sensing systems.     

Unstably stratified geophysical fluid dynamics

The linear dynamics of the unstably stratified geophysical flows is investigated with a two-layer formulation. A ‘convective’ deformation radius classifies the dynamics into three regimes:

• 1. 

  1. the scales smaller than the deformation radius: the dynamics characterized by unstable inertial-gravity modes;

• 2. 

  2. the scales larger than the deformation radius: a quasi-geostrophic regime;

• 3. 

  3. the scales close to the deformation radius, where the dynamics transits from the inertial-gravity regime to the quasi-geostrophic regime.

The Rossby wave can propagate eastward in the unstably stratified quasi-geostrophic regime. The baroclinic instabilities are basically realized as a larger-scale extent of the inertial-gravity instabilities, but the former can be isolated from the latter in a limit of small β-effect, with a very deep lower layer. The results suggest that the convectively unstable Jovian atmospheric dynamics can be well described as a quasi-geostrophic system.     

Analysis of Turbulence Collapse in the Stably Stratified Surface Layer Using Direct Numerical Simulation

The nocturnal atmospheric boundary layer (ABL) poses several challenges to standard turbulence and dispersion models, since the stable stratification imposed by the radiative cooling of the ground modifies the flow turbulence in ways that are not yet completely understood. In the present work we perform direct numerical simulation of a turbulent open channel flow with a constant (cooling) heat flux imposed at the ground. This configuration provides a very simplified model for the surface layer at night. As a result of the ground cooling, the Reynolds stresses and the turbulent fluctuations near the ground re-adjust on times of the order of L/u _τ , where L is the Obukhov length scale and u _τ is the friction velocity. For relatively weak cooling turbulence survives, but when Re_L=Lu_t/n <~100{Re_L=Lu_\tau/\nu \lesssim 100} turbulence collapses, a situation that is also observed in the ABL. This criterion, which can be locally measured in the field, is justified in terms of the scale separation between the largest and smallest structures of the dynamic sublayer.     

Eddy Covariance Tilt Corrections over a Coastal Mountain Area in South-east China: Significance for Near-Surface Turbulence Characteristics

Turbulence characteristics of an atmospheric surface layer over a coastal mountain area were investigated under different coordinate frames.Performances of three methods of coordinate rotation:double rotation(DR),triple rotation(TR),and classic planar-fit rotation(PF) were examined in terms of correction of eddy covariance flux.Using the commonly used DR and TR methods,unreasonable rotation angles are encountered at low wind speeds and cause significant run-to-run errors of some turbulence characteristics.The PF method rotates the coordinate system to an ensemble-averaged plane,and shows large tilt error due to an inaccurate fit plane over variable terrain slopes.In this paper,we propose another coordinate rotation scheme.The observational data were separated into two groups according to wind direction.The PF method was adapted to find an ensemble-averaged streamline plane for each group of hourly runs with wind speed exceeding 1.0 m s 1.Then,the coordinate systems were rotated to their respective bestfit planes for all available hourly observations.We call this the PF10 method.The implications of tilt corrections for the turbulence characteristics are discussed with a focus on integral turbulence characteristics,the spectra of wind-velocity components,and sensible heat and momentum fluxes under various atmospheric stabilities.Our results show that the adapted application of PF provides greatly improved estimates of integral turbulence characteristics in complex terrain and maintains data quality.The comparisons of the sensible heat fluxes for four coordinate rotation methods to fluxes before correction indicate that the PF10 scheme is the best to preserve consistency between fluxes.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

Turbulence frontogenesis

Summary The frontogenesis function in terms of the time derivative of the gradient of any relevant airborne quantity comprises all processes contributing to frontogenesis. Thus the various terms of this function are able to reveal processes of frontal development and their structure. Therefore the evaluation of these terms from measurements or in the frame of model simulations offers the chance of gaining more insight in frontal processes. If frontogenesis is evaluated from average basic data representative for a certain time-or space-scale, the result will be a kind of average frontogenesis, which naturally contains turbulence terms in the form of covariances. The processes described by these terms are called turbulence frontogenesis.This paper describes the basic formalisms of turbulence frontogenesis, offers cross-sections of these terms gained in experiments flown in sea-breeze fronts and gives some hints about their general behaviour.With 4 Figures