Large-scale Atmospheric Turbulence Research Articles

Mesoscale structure of the atmospheric boundary layer across a natural roughness transition

The structure and intensity of turbulence in the atmospheric boundary layer (ABL) drive fluxes of sediment, contaminants, heat, moisture, and CO[Formula: see text] at the Earth's surface. Where ABL flows encounter changes in roughness-such as cities, wind farms, forest canopies, and landforms-a new mesoscopic flow scale is introduced: the internal boundary layer (IBL), which represents a near-bed region of transient flow adjustment that develops over kilometers. Measurement of this new mesoscopic scale lies outside present observational capabilities of ABL flows, and simplified models fail to capture the sensitive dependence of turbulence on roughness geometry. Here, we use large-eddy simulations, run over high-resolution topographic data and validated against field observations, to examine the structure of the ABL across a natural roughness transition: the emergent sand dunes at White Sands National Park. We observe that development of the IBL is triggered by the abrupt transition from smooth playa surface to dunes; however, continuous changes in the size and spacing of dunes over several kilometers influence the downwind patterns of boundary stress and near-bed turbulence. Coherent flow structures grow and merge over the entire [Formula: see text]10 km distance of the dune field and modulate the influence of large-scale atmospheric turbulence on the bed. Simulated boundary stresses in the developing IBL counter existing expectations and explain the observed downwind decrease in dune migration, demonstrating a mesoscale coupling between flow and form that governs landscape dynamics. More broadly, our findings demonstrate the importance of resolving both turbulence and realistic roughness for understanding fluid-boundary interactions in environmental flows.

Исследование аэродинамических характеристик самолета при попадании в зону турбулентности ясного неба и вопросы безопасности полета

Shear flows in the atmosphere lead to formation of the clear-air turbulence (CAT) zones. These zones are having the characteristic horizontal size of 20 km to 2000 km and may be less than 1000 m thick making it difficult to detect them and create effective systems to find the bypass routes. Intense CAT zones could appear at the altitudes of up to 30 km and higher. The main CAT feature lies in the fact that it occurs not in the clouds, but in the clear sky with good visibility, where meteorological radar is unable to detect it, and the flight crew is unable to get prepared. Every year, about 750 cases of the aircraft entering the CAT zones are registered in the global civil aviation. This work constructs a grid solution that simulates the large-scale atmospheric turbulence based on the atmospheric profiles taken from the experiment within the framework of the boundary value problem for the Reynolds-averaged Navier – Stokes equations. On the basis of the obtained solution and within the frames of the engineering method, coherent vortex structures (CVS) are formed, interaction with which, assuming the hypothesis of the perturbed speed frozen field, makes it possible to evaluate possible increments in the aerodynamic forces and moments and to simulate a situation of the aircraft entering the CAT zones.

Buffeting response of a suspension bridge based on the 2D rational function approximation model for self-excited forces

In the last thirty years, the aerodynamic nonlinearities related to the slow variation of the angle of attack produced by large-scale atmospheric turbulence and their impact on the buffeting response of long-span suspension bridges have been a hot topic in wind engineering research. Self-excited forces accounting for such an effect of turbulence have been crucial in predicting the dynamic response of bridge sectional models subjected to multi-harmonic gusts. In contrast, only few studies on full suspension bridges in realistic turbulent flows are available. To fill this gap, the 2D RFA model for self-excited forces, recently developed and experimentally validated by the authors, in this paper is incorporated into a stochastic time-variant state-space framework to assess the nonlinear buffeting response of a suspension bridge. The most important feature of this model is the modulation of the self-excited forces due to the spatio-temporal fluctuation of the angle of attack produced by low-frequency turbulence. Moreover, the nonlinear external buffeting forces are formulated to achieve a reasonable compromise between the conflicting needs of modelling both nonlinear and unsteady effects of wind velocity fluctuations. The model is applied to the Hardanger Bridge in Norway, considering different wind conditions. Indeed, the aerodynamic derivatives of this bridge deck cross-section present a strong dependence on the mean angle of attack. The results emphasise the significant impact on the buffeting response and flutter stability of considering time-variant self-excited forces, though in specific cases the classical time-invariant approach is found to provide accurate predictions of the bridge vibrations. Finally, the paper investigates the sensitivity of the response statistics to the model cut-offs used to separate the low-frequency and the high-frequency turbulence bands.

Time-variant self-excited force model based on 2D rational function approximation

Large-scale atmospheric turbulence produces large-amplitude low-frequency fluctuations of the angle of attack, which can significantly change the self-excited forces acting on a bridge deck. Such a nonlinear effect must be carefully modelled for an accurate prediction of the dynamic response of long-span suspension bridges to the turbulent wind. By assuming that the angle of attack varies slowly, a time-variant linear model relying on Roger’s rational function approximation (RFA) of the force transfer function is proposed, and a formulation of the problem in the state space is outlined. In particular, an existing model is improved by a flexible fitting of the RFA directly in the multivariate space of reduced velocity and angle of attack. Another contribution of the present work is the setup of an experimental procedure based on bi- or multi-harmonic forced-vibration tests to underscore the variation of magnitude and phase of self-excited forces under a time-variant angle of attack. These wind tunnel tests also allowed a sound experimental validation of the proposed model, considering two quite different bridge deck cross-sections as case studies. Aerodynamic derivatives for various angles of attack were measured to determine the parameters of the model. Despite its simplicity, the model yields accurate results up to relatively fast variations of the angle of attack, and it can reproduce the complicated behaviour of the self-excited forces revealed by the experiments. The performance of the model strongly depends on the goodness of the RFA-based fitting of aerodynamic derivatives, and the excellent results obtained were possible thanks to the high flexibility of the proposed method.

Fluid–structure interaction simulation of floating structures interacting with complex, large-scale ocean waves and atmospheric turbulence with application to floating offshore wind turbines

We develop a numerical method for simulating coupled interactions of complex floating structures with large-scale ocean waves and atmospheric turbulence. We employ an efficient large-scale model to develop offshore wind and wave environmental conditions, which are then incorporated into a high resolution two-phase flow solver with fluid–structure interaction (FSI). The large-scale wind–wave interaction model is based on a two-fluid dynamically-coupled approach that employs a high-order spectral method for simulating the water motion and a viscous solver with undulatory boundaries for the air motion. The two-phase flow FSI solver is based on the level set method and is capable of simulating the coupled dynamic interaction of arbitrarily complex bodies with airflow and waves. The large-scale wave field solver is coupled with the near-field FSI solver with a one-way coupling approach by feeding into the latter waves via a pressure-forcing method combined with the level set method. We validate the model for both simple wave trains and three-dimensional directional waves and compare the results with experimental and theoretical solutions. Finally, we demonstrate the capabilities of the new computational framework by carrying out large-eddy simulation of a floating offshore wind turbine interacting with realistic ocean wind and waves.

Proposed form for the atmospheric turbulence spatial spectrum at large scales

The performance of large optical systems can be strongly influenced by the behavior of large-scale atmospheric turbulence. Previous optical phase difference data diverged from theoretical predictions based on von Kármán's model. To establish a better model microthermal data over large spatial scales were collected at two sites with few terrain inhomogeneities, in unstable midday conditions. Spatial structure function and spectra are developed. A model spatial spectrum is fit to the data with parameters to set two power law dependencies and the transition rate between them. By working with spatial spectral data the assumption of frozen flow is avoided. The optimum spatial spectrum is Kolmogorov-like in the inertial range. Temporal spectral data compare favorably with the new model, which better describes the transition of turbulence scaling from small scales to large.

Evaluation of a Fast-Running Urban Dispersion Modeling System Using Joint Urban 2003 Field Data

Abstract An urban dispersion modeling system was evaluated using the Joint Urban 2003 field data. The system consists of a fast-running urban airflow model (RUSTIC, for Realistic Urban Spread and Transport of Intrusive Contaminants) that is coupled with a Lagrangian particle transport and diffusion model (MESO) that uses random-walk tracer diffusion techniques. Surface measurements from fast-response and integrated bag samplers were used to evaluate model performance in predicting near-field (less than 1 km from the source) dispersion in the Oklahoma City, Oklahoma, central business district. Comparisons were made for six different intense operating periods (IOPs) composed of three different release locations and stable nighttime and unstable daytime meteorological conditions. Overall, the models were shown to have an underprediction bias of 47%. A possible influence to this underprediction is that the higher density of sulfur hexafluoride in comparison with air was not taken into account in the simulations. The models were capable of predicting 42% of the sampler data within a factor of 2 and 83% of the data within a factor of 10. When the effects of large-scale atmospheric turbulence were included, the models were shown to be capable of predicting 51% of the data within a factor of 2. The results were further broken down into performance for varying meteorological conditions. For daytime releases, the models performed reasonably well; for nighttime releases the models performed more poorly. Two possible causes of the poorer nighttime comparisons are (a) an inability to model the suppression of vertical turbulence because of the assumption of isotropy in RUSTIC’s k–ω turbulence model and (b) difficulty in modeling the light and variable inflow winds. The best comparisons were found for the three continuous daytime releases of IOP-4. It was hypothesized that these good comparisons were a result of steadier inflow conditions combined with the fact that the release site was more exposed and closer to the sodar used for the inflow meteorological conditions.

On the differences between 2D and QG turbulence

Due to their mathematical tractability,two-dimensional (2D) fluid equations are often used by mathematiciansas a model for quasi-geostrophic (QG) turbulence in the atmosphere,using Charney's 1971 paper as justification. Superficially, 2D and QGturbulence both satisfy the twin conservation of energy and enstrophyand thus are unlike 3D flows, which do not conserve enstrophy. Yet QGturbulence differs from 2D turbulence in fundamental ways, which arenot generally known. Here we discuss ingredients missing in 2Dturbulence formulations of large-scale atmospheric turbulence. Weargue that there is no proof that energy cannot cascade downscale inQG turbulence. Indeed, observational evidence supports a downscaleflux of both energy and enstrophy in the mesoscales.It is suggested that the observed atmospheric energy spectrum isexplainable if there is a downscale energy cascade of QG turbulence, butis inconsistent with 2D turbulence theories, which require an upscaleenergy flux. A simple solved example isused to illustrate some of the ideas discussed.

Relative particle motion in capillary waves.

When a container of fluid is oscillated vertically, capillary waves develop on the surface if the amplitude exceeds a critical value. Experimentally one finds that the motion of small particles on the surface of the fluid is close to Brownian. Here we study the relative motion of particle pairs. The experiment establishes that particle motion is strongly correlated over macroscopic distances. Our observations are in striking agreement with upper-ocean studies, and with theories that appear applicable to this ``weak turbulence'' problem, and in disagreement with experimental and theoretical results for two-dimensional large-scale atmospheric turbulence.

Power and cross— spectra for the turbulent atmospheric motion and transports in the domain of wave number frequency space: Theoretical aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross—spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.

Contour Dynamics Methods

Contour Dynamics Methods

Diurnal and Inter-Diurnal Variations in Large-Scale Atmospheric Turbulence Over Southern Africa

Abstract Hourly wind speeds at eighteen stations have been used to determine regional and seasonal diurnal and inter-diurnal wind variabilities in southern Africa. From the ratio of the diurnal/inter-diurnal variabilities the degree to which diurnal boundary layer processes dominate the near-ground windfield has been established and mapped in generalised form for the sub-continent at different times of year. Results show the predominance at all times of mesoscale effects over those of synoptic scale in the generation of large-scale atmospheric turbulence in the boundary layer.

Homogeneous and Isotropic Turbulence on the Sphere

Abstract The assumption that the streamfunction for two-dimensional nondivergent flow on the sphere is a homogeneous and isotropic random field is used to obtain a variety of results for the study of large-scale atmospheric turbulence. These results differ somewhat from those for Cartesian geometry. It is shown that the necessary and sufficient condition that the turbulent flow be homogeneous and isotropic is the statistical independence of the spherical harmonic expansion coefficients of the streamfunction and the dependence of the variance of the expansion coefficients only an the wavenumber n. The homogeneity and isotropy of the vorticity field and of the velocities along and perpendicular to the geodesic connecting points on the sphere follows. The usual zonal and meridional velocity components on the sphere are an-isotropic although, at a point, these velocity components are uncorrelated and have equal amounts of kinetic energy. Equations for the covariance function and the spectrum for flow on the s...

Atmospheric energy fluxes over Europe

Horizontal fluxes of atmospheric energy (sensible and latent heat, potential and kinetic energy) are computed at European aerological stations between the surface and the 150 mb level for the period 1974–1976. The fluxes are divided into their mean flow and transient eddy contributions. The main emphasis is given to the computed transient eddy fluxes and their physical and synoptic interpretation. The vertically integrated transient eddy fluxes of sensible heat and latent heat are essentially down-gradient and reflect the “mixing” caused by the large-scale atmospheric turbulence. The transient eddy flux of sensible heat in the upper troposphere over western Europe in winter is found to be southward and up-gradient. By using a simple averaging technique it is shown that this up gradient flux is due mainly to fluctuations with a period of less than 1 month. A synoptic example is presented showing a large-amplitude wave, typical in situations when formation of cut-off lows and shearlines takes place in the upper troposphere. In this case there is a negative spatial correlation between temperature and the meridional wind component. This kind of phenomenon, which is common over western Europe, is at least partially responsible for the observed up-gradient component of the sensible heat flux by transient eddies. DOI: 10.1111/j.2153-3490.1980.tb00977.x

Atmospheric energy fluxes over Europe

Horizontal fluxes of atmospheric energy (sensible and latent heat, potential and kinetic energy) are computed at European aerological stations between the surface and the 150 mb level for the period 1974–1976. The fluxes are divided into their mean flow and transient eddy contributions. The main emphasis is given to the computed transient eddy fluxes and their physical and synoptic interpretation. The vertically integrated transient eddy fluxes of sensible heat and latent heat are essentially down-gradient and reflect the “mixing” caused by the large-scale atmospheric turbulence. The transient eddy flux of sensible heat in the upper troposphere over western Europe in winter is found to be southward and up-gradient. By using a simple averaging technique it is shown that this up gradient flux is due mainly to fluctuations with a period of less than 1 month. A synoptic example is presented showing a large-amplitude wave, typical in situations when formation of cut-off lows and shearlines takes place in the upper troposphere. In this case there is a negative spatial correlation between temperature and the meridional wind component. This kind of phenomenon, which is common over western Europe, is at least partially responsible for the observed up-gradient component of the sensible heat flux by transient eddies. DOI: 10.1111/j.2153-3490.1980.tb00977.x

A note on eulerian-Lagrangian time scale transformation for large-scale atmospheric turbulence

An expression for the transformation parameter for the Eulerian-Lagrangian time scale transformation is derived for the large-scale atmospheric turbulence through integral time scale approach.

On the large-scale atmospheric turbulence

The dynamical equations of the velocity correlation and spectrum functions for three-dimensional anisotropic turbulence in a stratified, rotating atmosphere are derived and discussed. The characteristics of the horizontal two-dimensional isotropic turbulence are analyzed.

Dependence of the Highly Truncated Spectral Vorticity Equation on Initial Conditions

Abstract The analytic solutions in time to the highly truncated (low-order) spectral vorticity equation, involving the nonlinear interaction of one planetary wave with an arbitrary zonal flow, have been investigated for a wide variety of initial conditions which span the range of atmospheric observations. These conditions include both a characteristic mean wintertime zonal jet, a simulated double jet, all planetary waves from wavenumbers 1–12, and various wave configurations for wavenumber 3. The results show wide variability in solutions from configurations which are almost independent in time to those which describe highly elliptic oscillations. There is no systematic dependence of nonlinearity on total energy amplitude of the system nor do small initial perturbations necessarily imply quasi-linearity. The solutions described for this simple model exemplify the extreme complexity of large-scale atmospheric turbulence.

A study of large-scale atmospheric turbulent kinetic energy in wave-number frequency space

Large-scale atmospheric turbulence is examined through the application of a wave-number frequency Fourier analysis of the velocity distributions on latitude circles. The primary advantage of the wave-number frequency energy spectra is that it permits analysis of the transient eddies in terms of their length scale and in terms of the speed and direction of their motion. Thus, the relative importance of retrogressing waves may be considered in the analysis. The kinetic energy spectra of the meridional component of velocity is found to contain a distinct band of energy for each wave number which shifts to higher negative frequencies as wave number increases from 4 through 10, at 40° N during winter season 1964. This indicates that the motion of these waves is predominantly from west to east. During the summer season, waves moving in the opposite direction carry a relatively large portion of the transient eddy kinetic energy. The terms of the component form of the kinetic energy equations in wave-number frequency space are evaluated with horizontal nondivergent velocities. The form of the equations used involves nonlinear interaction terms, which represent an inertial transfer process; ageostrophic terms, which represent the work done by the pressure and Coriolis forces; and the eddy frictional terms. Of the nonlinear interaction terms, the one which provides the largest positive or negative contribution to the spectral energy is the inertial term involving the longitudinal derivative. The largest interaction combination within each of these terms involves the spectral components of the kinetic energy production terms. This condition causes a positive contribution to the energy of waves moving from west to east and a negative contribution to waves moving from east to west. The contributions to the spectral energy through the interaction terms involving latitudinal derivatives are smaller with less consistency in sign. The interaction combinations representing the kinetic energy production in these terms have the same magnitude as several other interaction combinations. The contributions from the ageostrophic terms serve to balance the contributions from the interaction terms. The magnitude of these balancing contributions is from 2 to 5 times the magnitude of the spectral energy. DOI: 10.1111/j.2153-3490.1969.tb00484.x

An analysis of the geostrophic kinetic energy spectrum of large-scale atmospheric turbulence

The mean geostrophic kinetic energy spectrums of the large-scale atmospheric circulation features are presented for a 6-month winter period for three elevations at three latitudes. The mean spectrums are partitioned into two sections, and an 8/3 power relationship is noted between geostrophic kinetic energy and wavelength for the higher wave numbers. The physical significance of the partitioning and of the 8/3 relationship is considered by comparing these results with the results obtained from other investigations of atmospheric energy processes. Certain comparisons indicate that the wavelengths described by the 8/3 power relationship are those for which the two-dimensional turbulence is isotropic. Other comparisons suggest that these same wavelengths are those at which the kinetic energy of the atmosphere is produced.