On wavelet analysis of nonstationary turbulence

Wavelets are new tools for turbulence analysis that are yielding important insights into boundary-layer processes. Wavelet analysis, however, has some as yet undiscussed limitations: failure to recognize these can lead to misinterpretation of wavelet analysis results. Here we discuss some limitations of wavelet analysis when applied to nonstationary turbulence. Our main point is that the analysis wavelet must be carefully matched to the phenomenon of interest, because wavelet coefficients obscure significant information in the signal being analyzed. For example, a wavelet that is a second-difference operator can provide no information on the linear trend in a turbulence signal. Wavelet analysis also yields no meaningful information about nonlinear behavior in a signal — contrary to claims in the literature — because, at any instant, a wavelet is a single-scale operator, while nonlinearity involves instantaneous interactions among many scales.     

A study of intermittent turbulence with cases-99 tower measurments

Characteristics of intermittent turbulence events in the stably stratified nocturnal boundary layer are investigated with data collected in the CASES-99 tower array of 300-m radius. The array consists of a central 60-m tower with eddy covariance measurements at eight levels and six satellite towers with eddy covariance measurements at 5 m. A significant increase in the magnitude of vertical wind velocity () and spectral information are used to define the onset of an intermittent turbulence event. Normally, only a subset of 5 m-levels in the tower network experience an intermittent turbulence event concurrent with one at the 5 m-level on the main tower. This behaviour reveals the small horizontal extent of most events. Intermittent turbulence events at the main tower 5-m level are normally confined to a layer much thinner than the 60-m tower height. The turbulent kinetic energy budget is evaluated for intermittent turbulence events observed at the 5-m level on the main tower. Generally, the onset of an intermittent turbulence event is not closely related to the reduction of the gradient Richardson number below 0.25, the critical Richardson number of turbulence generation for linear instability. Possible explanations including the influence of advected turbulence patches are discussed.     

Characteristics of intermittent turbulence in the upper stable boundary layer over Greenland

The experiment IGLOS (Investigation of the Greenland Boundary Layer Over Summit) was conducted in June and July 2002 in the central plateau of the Greenland inland ice. The German research aircraft Polar2, equipped with the turbulence measurement system Meteopod, was used to investigate turbulence and radiation flux profiles near research station “Summit Camp”. Aircraft measurements are combined with measurements of radiation fluxes and turbulent quantities made from a 50 m tower at Summit Camp operated by Eidgenössische Technische Hochschule (ETH) Zürich. During all six flight missions, well-developed stable boundary layers were found. Even in high-wind conditions, the surface inversion thickness did not exceed roughly 100 m. The turbulent height of the stable boundary layer (SBL) was found to be much smaller than the surface inversion thickness. Above the surface layer, significant turbulent fluxes occurred only intermittently in intervals on the order of a few kilometres. Turbulent event fraction in the upper SBL shows the same dependence on gradient Richardson number as reported for near-surface measurements. Clear-air longwave radiation divergence was always found to contribute significantly to the SBL heat budget. In low-wind cases, radiative cooling even turned out to be dominant.     

Measurements of turbulence and fossil turbulence near ampere seamount

Measurements of temperature and velocity microstructure near and downstream of a shallow seamount are used to compare fossil turbulence versus non-fossil turbulence models for the evolution of turbulence microstructure patches in the stratified ocean. According to non-fossil oceanic turbulence models, all overturn length scales L_T of the microstructure grow and collapse in constant proportion to each other and to the turbulence energy (Oboukov) scale L_O and the inertial buoyancy (Ozmidov) scale of the patches; that is, with L_Trms ≈1.2L_R and viscous dissipation rate ≈ ₀^*. According to the Gibson fossil turbulence model, all microstructure originates from completely active turbulence with ₀ ≈ 3L_T²N³(≈ 28₀^*) and L_{T/√6 ≈ LTrms}, but this rapidly decays into a more persistent active-fossil state with _0F ≈ 30vN², where N is the buoyancy frequency and v is the kinematic viscosity and, without further energy supply, finally reaches a completely fossil turbulence hydrodynamic state of internal wave motions, with _F. The last turbulence eddies, with ≈ _F, vanish at a buoyant-inertial-viscous (fossil Kolmogorov) scale L_KF that is much smaller than the remnant overturn scales L_T for large ₀/_F ratios. These density, temperature, and salinity overturns with L_T ≈ 0.6 L_R0 0.6 L_R persist as turbulence fossils (by retaining the memory of _o) and collapse very slowly. In the near wake below the summit depth of Ampere seamount, a much larger proportion of completely active turbulence patches was found than is usually found in the ocean interior away from sources. Dissipation rates and turbulence activity coefficients of microstructure patches were found to decrease downstream, suggesting that the active turbulence indicated by the patches with A_T 1 was caused by the presence of the seamount as a turbulence source. Therefore, the turbulence and mixing processes of ocean layers far away from turbulence sources probably have been undersampled by microstructure data sets lacking any A_T 1 patches. This is because large fractions of the mixing and viscous dissipation of the patches occur in short-lived active turbulence regimes that are too brief to be detected. Consequently, large underestimates of the true space-time average turbulence fluxes and turbulence and scalar dissipation rates may result if non-fossil turbulence models are assumed in ocean microstructure data interpretation.     

湍流的分子动力学理论

湍流是自然界中极为普遍的一种流体运动形态。研究湍流运动发生发展的规律,在气象学、海洋学、空间物理、流体力学、等离子体物理以及不少工程技术等领域中,不仅具有重要的实用价值,而且是一个极有意义的理论问题,也一直引起各方面的密切注视。湍流理论的系统研究已有五十多年的历史,其主要成果大多建立于三十年代和四十年代初期。以后一个时期内,由于问题的复杂和困难,进展并不显著。近几年来,国内外对湍流     

Intermittency of turbulence within open canopies

Eddy covariance data have been analyzed to examine intermittency and clustering properties of turbulence within open canopies. Intermittency consists of two aspects: one is related to amplitude variation and the other to clustering. Using the telegraph approximation (TA), the clustering properties have been separated from amplitude effects. Intermittency of canopy turbulence has been explored via clustering exponent, probability density distribution of inter-pulse period of TA, intermittency exponent and structure kurtosis. Intermittency and clustering properties of turbulence within open canopies show similar features to those within dense canopy but some differences are also noted. Unlike within a dense canopy, temperature does not show larger clustering than velocity, which seems to be due to a different thermal structure of the sub-canopy and larger vertical scale of canopy eddy within open canopies. Within the crown region, the inter-pulse probability distribution of TA does not show the ‘double regime’ which was observed within the crown of a dense canopy, indicating less influence of near-field source on canopy turbulence within open canopies. For TA series of the flow variables, intermittency exponent is higher for temperature than for two velocity components within open canopies, which are opposite within a dense canopy. When comparing intermittency for flow variables and their TA series, it is shown that amplitude variation mitigates intermittency for both velocity components and temperature although amplitude variations play a much larger role in velocity intermittency than in temperature counterpart. Kurtosis analysis demonstrates that structure kurtosis is higher at large scales in stable conditions than in unstable conditions, indicating the existence of global intermittency due to stable stratification. The intermittency features of canopy turbulence within open canopies have been discussed in comparison with those within a dense canopy.     

A case study of severe clear-air turbulence

Summary On January 19, 1961, 1816 MST (=January 20, 0116 GCT), a B-52 aircraft was lost in severe clear-air turbulence (CAT) over northwestern New Mexico. This report describes the weather conditions in the upper troposphere and lower stratosphere at the time of the accident. A working hypothesis on the formation of CAT proposed in previous papers is in good agreement with the data presented here.

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Zusammenfassung Am 19. Januar 1961 um 1816 Mountain Standard Time (=20. Januar 1961, 0116 GCT) verursachte eine schwere Clear-Air-Turbulenz (CAT) über Nordwest-Neumexiko, USA, den Verlust eines Flugzeuges vom Typ B-52. Der vorliegende Bericht beschreibt die Witterungsbedingungen in der oberen Troposphäre und der unteren Stratosphäre zur Zeit des Unfalls. Eine Arbeitshypothese über das Zustandekommen von Clear-Air-Turbulenz, die in früheren Veröffentlichungen dargelegt wurde, steht in guter Übereinstimmung mit den hier vorgelegten Daten.

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Résumé Une très forte turbulence en air clair (CAT) a provoqué la chute d'un avion du type B-52 sur le Nouveau-Méxique (Etats-Unis); ce phénomène s'est produit le 19 janvier 1961 à 18 h 16 «Mountain Standard Time» (=20 janvier 1961 à 01 h 16 GMT). Le présent mémoire décrit les conditions météorologiques régnant au moment de l'accident et cela aussi bien dans la haute troposphère que dans la stratosphère inférieure. Une hypothèse de travail décrite dans de précédentes publications, hypothèse concernant l'apparition de «Clear-Air-Turbulence» (CAT), correspond très bien aux conditions spéciales décrites ici.

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With 4 Figures

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This report has been prepared under Contract No. N 189(188) 55120 A with U.S. Navy Weather Research Facility.     

Urban-scale variations of turbulence parameters and fluxes

Sensible heat (H) and latent heat (LE) fluxes and turbulence statistics in St. Louis, Missouri and the surrounding region are presented. The urban-scale analyses were derived from a series of aircraft transects at 150 m above ground across the metropolitan area during the afternoon convective period. The results revealed that H varied by a factor of two to four in the region; the largest values were associated with the urban heat island. LE varied across the urban area by about a factor of four, but low values of LE overlaid the urban heat island. Consequently, the Bowen ratio (H/LE) exhibited large spatial variability, with a maximum value greater than 1.5 over the city and values less than 0.2 in nonurban areas. The areas along the Mississippi River and adjacent low lying marshland northeast of the downtown area displayed significantly smaller H and Bowen ratio. The derived surface heat storage term (G) for this area as well as for the urban area exceeded either H or LE.The spatial patterns for the standard deviations of the three velocity components ( _u,v,w ), temperature ( _T ), and absolute humidity ( _q ), are also presented. The patterns of _u,v,w were similar to the pattern of H. the highest values associated with the urban heat island. The correlation coefficient between the vertical velocity and temperature fluctuations was highest over the city, and a noteworthy minimum was observed in the upwind area over the river and marshland in association with low H. The convective similarity relationships for _u,v,w appeared to be approximately valid spatially, as variations were typically less than 10% from theory over the urban area and nonurban region, except for a 40% anomaly in the lowland around the river northeast of the city.Measurements of H from 30-m towers within various land-use areas were contrasted with the aircraft data. Land-use differences in H at the surface were at least as large as those observed at 150 m across the city. This was primarily because of the measurement requirement that the minimum resolvable fetch increases with measurement height.     

Statistical description of anisotropic and inhomogeneous turbulence

Statistical functions such as correlation functions and spectra yield length scales, each of which describes a certain aspect of the large-scale structure of turbulence. In this study not only statistics of wind fluctuations measured at the same place have been analysed but also statistics of fluctuations at different heights. Thus a spatial picture of the energy-containing and the momentum-transporting eddies has been obtained and some features of the momentum transport are described.     

Experimental investigation of atmospheric boundary layer turbulence

This paper describes how to measure turbulence in the atmospheric boundary layer (ABL) in order to address certain problems in modern atmospheric physics. These problems mainly relate to the Earth's energy budget (including the hydrological cycle) and biogeochemical cycles. Starting from the main characteristic numbers and the basic equations of atmospheric turbulent flow, we show what turbulence parameters are important to measure. Special attention is given to the various methods used to compute the turbulent fluxes. We analyse the range of scales which has to be measured to properly capture the eddies contributing to the turbulent transfers. This range of scales determines what sensors can be used in the atmospheric surface layer and in the ABL. We describe the most widely used instruments and their performances. The principal platforms used to deploy these instruments are examined. Aircraft are described in more details, because they allow a thorough exploration of the ABL. In the last section, some examples of ABL turbulence signals measured in various conditions are presented. These examples illustrate horizontally homogeneous turbulence as well as inhomogeneous signals for which standard analysis techniques cannot be used. We show how some recent techniques, like wavelet transforms, can help to investigate this kind of signal. At the end, we present what would be interesting to do in the near future for the study of ABL turbulence.     

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.     

Propeller anemometers as sensors of atmospheric turbulence

Even though propeller anemometers are found to give outputs which deviate from the desired cosine relationship by an amount which varies with wind speed, their overall performance is consistent with many atmospheric requirements. Their output per unit wind speed is a function of angle of attack, such that when used as sensors of the vertical or horizontal cross-wind components in the atmosphere, calibration factors may differ by as much as 30 % from those obtained in a normal wind-tunnel calibration procedure (in which wind velocity is parallel to the anemometer shaft). These characteristics are sufficiently important that great care should be taken in using these devices inu-v-w orthogonal arrays.For use in eddy-correlation equipment, it appears that it is best to vane-mount the horizontal sensor to ensure that the appropriate calibration factor is employed.The response lengths of propeller anemometers also vary with angle of attack. Near=0 °, the axially-referred response length appears to depend linearly on cos, but near=90 ° a dependence on cos^1/2 fits the data. No strong effect of wind speed is found.Due to their limited response characteristics, these anemometers give rise to underestimates of the Reynolds stress measured near the surface. The extent of the loss is about 8 % when anemometers in good condition are employed at a height of 5m. Operation at a greater height would allow this error to be reduced. After exposure in the atmosphere for some time, the anemometers tend to respond more slowly and greater losses (of the order 25 %) can occur. Some improvement in performance is possible by the choice of a suitable spatial separation of the sensors.     

The inverse cascade range of quasi-geostrophic turbulence

Summary The homogeneous form of the quasi-geostrophic equations are examined from the perspective of the statistical theory of turbulence, utilizing the eddy-damped, Markovian quasinormal EDMQN approximation. After describing the historical origin of this procedure, together with some of its qualitative physics, we focus on an application to the large scales of the mesoscale. The specific problem investigated is an inverse cascade in which the energy source is at the small, thunderstorm-scale range, and the scales considered are all those larger than the forcing scale. We examine in particular the issue of the degree of anisotropy (in stretched coordinates) of the flow, the dependence of the flow on forcing and dissipation, and the applicability of the concept of negative eddy viscosity for the quasi-geostrophic equations.With 3 FiguresThe National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Roughness effects on urban turbulence parameters

Urban roughness lengths are estimated from measurements of u and u _* at one level under neutral conditions, assuming a logarithmic form for the vertical profile of wind velocity. At a given location in the urban area, estimated values show considerable directional variation. The dependence of some turbulence parameters on the urban roughness lengths is experimentally investigated during near-neutral conditions. The ratios _i /u _* decrease with roughness whereas the turbulence intensities _i /u increase with it. The dependence on roughness is not the same for all components.     

Characterizing the severe turbulence environments associated with commercial aviation accidents. A real-time turbulence model (RTTM) designed for the operational prediction of hazardous aviation turbulence environments

Summary In this paper, we will focus on the real-time prediction of environments that are predisposed to producing moderate-severe (hazardous) aviation turbulence. We will describe the numerical model and its postprocessing system that is designed for said prediction of environments predisposed to severe aviation turbulence as well as presenting numerous examples of its utility. The purpose of this paper is to demonstrate that simple hydrostatic precursor circulations organize regions of preferred wave breaking and turbulence at the nonhydrostatic scales of motion. This will be demonstrated with a hydrostatic numerical modeling system, which can be run in real time on a very inexpensive university computer workstation employing simple forecast indices. The forecast system is designed to efficiently support forecasters who are directing research aircraft to measure the environment immediately surrounding turbulence. The numerical model is MASS version 5.13, which is integrated over three different grid matrices in real-time on a university workstation in support of NASA-Langley’s B-757 turbulence research flight missions. The model horizontal resolutions are 60, 30, and 15 km and the grids are centered over the region of operational NASA-Langley B-757 turbulence flight missions. The postprocessing system includes several turbulence-related products including four turbulence forecasting indices, winds, streamlines, turbulence kinetic energy, and Richardson numbers. Additionally there are convective products including precipitation, cloud height, cloud mass fluxes, lifted index, and K-index. Furthermore, soundings, sounding parameters, and Froude number plots are also provided. The horizontal cross section plot products are provided from 16,000–46,000 feet in 2,000 feet intervals. Products are available every three hours at the 60 and 30 km grid interval and every 1.5 hours at the 15 km grid interval. The model is initialized from the NWS ETA analyses and integrated two times a day.     

Dispersion in sheared Gaussian homogeneous turbulence

By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(x_i, u_i, t) for the position (x _i) and velocity (u _i) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.     

Boundary-layer turbulence spectra in stable conditions

Simultaneous measurements of horizontal and vertical wind speeds and temperature fluctuations at heights up to 91 m in the stable atmospheric boundary layer are described. The power and cospectral shapes show a low-frequency peak (near the Brunt-Väisälä frequency) separated by a spectral gap from a peak at high frequency due to turbulence. Spectral shapes in the turbulence subrange at 8 m are in good agreement with the universal curves previously presented by Kaimal (1973). Further information is given on the variation of the scaling parameter, f ₀, with stability; and the applicability of the normalising procedure to the spectra from the higher levels is discussed.