Height-dependent Wind Research Articles

Estimation of Dynamic Wind Shear Coefficient to Characterize Best Fit of Wind Speed Profiles under Different Conditions of Atmospheric Stability and Terrains for the Assessment of Height-Dependent Wind Energy in Libya

Estimation of Dynamic Wind Shear Coefficient to Characterize Best Fit of Wind Speed Profiles under Different Conditions of Atmospheric Stability and Terrains for the Assessment of Height-Dependent Wind Energy in Libya

Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer

In this study, a numerical solution for degenerate space–time fractional advection–dispersion equations is proposed to simulate atmospheric dispersion in vertically inhomogeneous planetary boundary layers. The fractional derivative exists in a Caputo sense. We establish the maximum principle and a priori estimates for the solutions. Then, we construct a positivity-preserving finite-difference scheme, using monotone discretization in space and L1 approximation on the non-uniform mesh for the time derivative. We use appropriate grading techniques for the time–space mesh in order to overcome the boundary degeneration and weak singularity of the solution at the initial time. The computational results are demonstrated on the Gaussian fractional model as well on the boundary layers defined by height-dependent wind flow and diffusitivity, especially for the Monin–Obukhov model.

Nonparametric copula modeling of wind speed-wind shear for the assessment of height-dependent wind energy in China

The joint probability density function can quantitatively describe the statistical characteristics and correlation features between wind speed and shear; this forms the theoretical basis for assessing height-dependent wind energy. Here, a nonparametric copula-based joint probability model of wind speed-wind shear is developed to assess height-dependent wind energy in China. Utilizing the transformation method and optimal bandwidth algorithms, a nonparametric copula model for wind speed/wind shear correlation analysis is proposed. Joint probability density models of wind speed and wind shear are then constructed. Various copula and marginal density models (including single parametric, mixture parametric, and kernel density estimation models) are evaluated at the regional scale. The nonparametric copula model exhibits remarkable superiority and is therefore deemed to be more suitable for wind speed/wind shear correlation analysis and joint probability modeling. When assessing height-dependent wind energy, the average distributions of wind turbine power output and capacity factor are obtained across mainland China. Additionally, this model could accurately analyze variations in wind power density with respect to hub height. These results can effectively facilitate accurate micro-site selection, thereby economically benefiting wind farms.

Estimating the environmental impacts of HVDC and UHVDC lines for large-scale wind power transmission considering height-dependent wind and atmospheric stability

Due to the imbalance of China’s resources allocation, inter-provincial high voltage direct current (HVDC) transmission grid is considered to be the promising solution to solve to the large-scale wind power transmission, which could tackle the reverse regional distribution problem of energy resource and electricity load. In this contribution, a power law profile model of wind speed on embedded atmospheric stability is developed for calculating the height-dependent wind speed. The Monin-Obukhov length is introduced to determine the atmospheric stability. The ion flow environment model considering height-dependent wind speed is proposed to estimate the influence of height-dependent wind on ground-level electric field environment of DC transmission line and the iterative flux tracing method-finite difference is proposed to solve the model. It is observed that the stable, neutral and unstable atmospheric conditions have a large influence on transverse wind speed and then indirectly influence the electric field and ion current environment of DC lines. For the electromagnetic environment of the practical DC line used for the wind power transmission, the proposed model provides a reasonable agreement with measurements from a perspective of practical engineering application.

Investigation of Interference Effects Between Wind Turbine and Spar-Type Floating Platform Under Combined Wind-Wave Excitation

In order to further understand the coupled aero-hydrodynamic performance of the floating offshore wind turbine (FOWT) in realistic ocean environment, it is necessary to investigate the interference effects between the unsteady aerodynamics of the wind turbine and different degree-of-freedom (DOF) platform motions under combined wind-wave excitation. In this paper, a validated CFD analysis tool FOWT-UALM-SJTU with modified actuator line model is applied for the coupled aero-hydrodynamic simulations of a spar-type FOWT system. The aero-hydrodynamic characteristics of the FOWT with various platform motion modes and different wind turbine states are compared and analyzed to explore the influence of the interference effects between the wind turbine and the floating platform on the performance of the FOWT. The dynamic responses of local relative wind speed and local attack angle at the blade section and wind-wave forces acting on the floating platform are discussed in detail to reveal the interaction mechanism between the aerodynamic loads and different DOF platform motions. It is shown that the surge motion and the pitch motion of the floating platform both significantly alter the local attack angle, while only the platform pitch motion have significant impacts on the local relative wind speed experienced by the rotating blades. Besides, the shaft tilt and the pro-cone angle of the wind turbine and the height-dependent wind speed all contribute to the variation of the local attack angle. The coupling between the platform motions along different DOFs is obviously amplified by the aerodynamic forces derived from the wind turbine. In addition, the wake deflection phenomenon is clearly observed in the near wake region when platform pitch motion is considered. The dynamic pitch motion of the floating platform also contributes to the severe wake velocity deficit and the increased wake width.

Modeling the development of hydrogen vapor cloud considering the presence of air humidity

A three-dimensional CFD model for large-scale liquid hydrogen spills is developed and validated by the experiments carried out by NASA. The effect of humidity on the development of hydrogen vapor cloud is emphasized, with the modified expressions of Lee model accounting for the phase changes of water and hydrogen. The results show that the numerical prediction is more consistent with the experiment considering the presence of air humidity. The condensation of water in the atmosphere increases the buoyancy of the vapor cloud, and promotes the diffusion of the cloud in vertical direction. The dimension of the cloud in streamwise direction changes little under different humidity, due to the balance between the height-dependent wind speed and the induced buoyancy. The scope of visible cloud indicated by the condensed water vapor expands with the increasing air humidity, and still lies within the flammable domain when the relative humidity approaching to 75%. Water vapor condensation induces the cloud temperature rise under the same concentration, and the leeward part is more influenced compared with the upwind part.

Development of a statistical bivariate wind speed-wind shear model (WSWS) to quantify the height-dependent wind resource

The goal of this study was to develop a statistical bivariate wind speed-wind shear model (WSWS). The development of WSWS is based on near surface wind speed data available from 397 measurement stations distributed over Germany, as well as on ERA-Interim reanalysis wind speed data available in 1000m above ground level (a.g.l.). These data were used (1) to calculate empirical distributions of wind speed in 1000ma.g.l., (2) empirical distributions of the wind shear exponent, and (3) to fit theoretical distributions to the empirical wind speed and wind shear exponent distributions. It was found that the four parameter Johnson SB distribution reproduces the shape of the wind speed in 1000ma.g.l. empirical distributions best. The four parameter Dagum distribution provided good fits to the empirical wind shear distributions. The parameterized wind speed and wind shear marginal distributions were then linked by 16 joint copulas. Goodness-of-fit evaluation of the joint copulas demonstrates that the Gaussian-Gaussian copula reproduces the empirical bivariate wind speed-wind shear distribution most accurately. By using WSWS it is possible to continuously calculate the wind speed probability density function in hub heights between 10ma.g.l. and 200ma.g.l. This allows WSWS to be applied to virtually any power curve for computing the wind energy yield and capacity factor in the analyzed hub height range. A one-time site-specific parametrization of WSWS is sufficient for a comprehensive height-dependent exploitation of the available wind resource.

Statistical Downscaling of Air Dispersion Model Using Neural Network for Delhi

ABSTRACTStatistical downscaling methods are used to extract high resolution information from coarse resolution models. The accuracy of a modelling system in analyzing the issues of either continuous or accidental release in the atmosphere is important especially when adverse health effects are expected to be found. Forecasting of air quality levels are commonly performed with either deterministic or statistical. In this study, statistical downscaling approach is investigated for hourly PM10 (particulate matter with aerodynamic diameter < 10 µm) pollutant for Delhi. The statistical downscaling is used on air dispersion model using neural network technique. The air dispersion model is based on analytical solution of advection diffusion equation in Neumann boundary condition for a bounded domain. Power laws are assumed for height dependent wind speed; and downwind and vertical eddy diffusivities are considered as an explicit function of downwind distance and vertical height. The predicted concentration of dispersion model with meteorological variables is used as input parameters to the neural network. It is found that performance of both air dispersion model and “pure” statistical models is inferior to that of the statistical downscaled model. In particular the root mean squares error (RMSE) of the deterministic model is reduced by at least 35% and 45% for hourly and rush hours particulate matter concentrations respectively using statistical downscaling. In addition, the results with statistical downscaled method show that the errors of the forecasts are reduced by at least 30% for stable and unstable-neutral atmospheric conditions.

Implications of Stably Stratified Atmospheric Boundary Layer Turbulence on the Near-Wake Structure of Wind Turbines

Turbulence structure in the wake behind a full-scale horizontal-axis wind turbine under the influence of real-time atmospheric inflow conditions has been investigated using actuator-line-model based large-eddy-simulations. Precursor atmospheric boundary layer (ABL) simulations have been performed to obtain mean and turbulence states of the atmosphere under stable stratification subjected to two different cooling rates. Wind turbine simulations have revealed that, in addition to wind shear and ABL turbulence, height-varying wind angle and low-level jets are ABL metrics that influence the structure of the turbine wake. Increasing stability results in shallower boundary layers with stronger wind shear, steeper vertical wind angle gradients, lower turbulence, and suppressed vertical motions. A turbulent mixing layer forms downstream of the wind turbines, the strength and size of which decreases with increasing stability. Height dependent wind angle and turbulence are the ABL metrics influencing the lateral wake expansion. Further, ABL metrics strongly impact the evolution of tip and root vortices formed behind the rotor. Two factors play an important role in wake meandering: tip vortex merging due to the mutual inductance form of instability and the corresponding instability of the turbulent mixing layer.

A MODEL FOR THE SIMULATION OF CROSSWIND INTEGRATED CONCENTRATIONS IN THE SURFACE-BASED INVERSION LAYER

A dispersion model for the estimation of crosswind integrated concentrations in the surface-based inversion is proposed. The generalized forms of eddy diffusivity with spatial dependence in both horizontal and vertical directions and vertical height-dependent wind speed are considered. In view of the computational limitation associated with numerical models for Dirac-delta function, the source term is expressed as a limiting case of normal distribution. The accuracy of the employed numerical scheme to solve the resulting partial differential equation with appropriate physically relevant boundary conditions is checked with those obtained from the respective analytical solutions available in literature for the particular forms of eddy diffusivity and wind speed. Concentrations computed from the proposed model are found close to those obtained from analytical models. The concentrations obtained from the proposed model are evaluated for the generalized functional forms of eddy diffusivity (Degrazia and Moraes, 1992; Degrazia et al., 2001) and diabatic logarithmic profile as well as power-law profile of wind speed with the observations from Hanford (Doran et al., 1984) and Copenhagen (Gryning and Lyck, 1984) diffusion experiments in stable and unstable conditions, respectively. Majority of the cases i.e., 64% and 96% are predicted in factor of two to observations in both stable and unstable conditions, respectively.

Analytical solution of the advection-diffusion equation for a ground-level finite area source

An advection-diffusion equation for a ground-level finite area source is solved analytically in a closed form using the superposition method. Power laws are assumed for height-dependent wind speed and vertical eddy diffusivity and for the downwind distance-dependent standard deviation of concentration distribution in the lateral direction. Results of the analysis show that the ground-level concentration increases with increasing downwind distance inside the source region and then decreases rapidly beyond the downwind edge of the source region. The ground-level concentration inside the source region is sensitive to exponents in the power laws for wind speed and vertical eddy diffusivity, while the ground-level concentration outside the source region is sensitive to the standard deviation of concentration distribution in the lateral direction. The solution for the ground-level finite area source is compared with solutions for a laterally infinite area source and a point source. The ratio of the ground-level concentration for the finite area source to that for the laterally infinite area source is highly dependent on lateral eddy diffusivity but almost independent of exponents in the power laws for wind speed and vertical eddy diffusivity. This is also true for the ratio of the ground-level concentration for the finite area source to that for the point source.

A Simplified Fourier Method for Nonhydrostatic Mountain Waves

Abstract A previously derived approximation to the standard Fourier integral technique for linear mountain waves is extended to include nonhydrostatic effects in a background flow with height-dependent wind and stratification. The approximation involves using ray theory to simplify the vertical eigenfunctions. The generalization to nonhydrostatic waves requires special treatment for resonant modes and caustics. Resonant modes are handled with a small amount of damping, and caustics are handled with a uniformly valid approximation involving the Airy function. This method is developed for both two- and three-dimensional flows, and its results are shown to compare well with an exact analytical result for two-dimensional mountain waves and with a numerical simulation for two- and three-dimensional mountain waves.

Traveltimes for infrasonic waves propagating in a stratified atmosphere

SUMMARY The tau‐p method of Buland & Chapman (1983) is reformulated for sound waves propagating in a stratified atmosphere under the influence of a height-dependent wind velocity profile. For a given launch angle along a specified azimuth, the ray parameter is redefined to include the influence of the horizontal wind component along the direction of wave propagation. Under the assumption of negligible horizontal wind shear, the horizontal wind component transverse to the ray propagation does not aVect the direction of the wave normal, but displaces the reference frame of the moving wavefront, thus altering the observed incidence azimuth. Expressions are derived for the time, horizontal range, and transverse range of the arriving waves as a function of ray parameter. Algorithms for the location of infrasonic wave sources using the modified tau‐p formulation in conjunction with regional atmospheric wind and temperature data are discussed.

Climatology of mesospheric gravity wave activity over Urbana, Illinois (40°N, 88°W)

A 5‐year (1991–1995) climatology of mesospheric gravity wave activity observed with the Urbana medium frequency (MF) radar is presented. We focus on the monthly mean horizontal wind variances associated with gravity waves with observed periods between 10 min and 8 hours. These results are compared with the seasonal characteristics from other gravity wave observations. The total wave variance, , displays a dominant semiannual variation (maxima summer/winter, minima spring/fall) below 87 km with little seasonal variation above 87 km. The zonal wave variance exceeds the meridional wave variance, , except around regions of zonal wind reversal. In all seasons the observed variance scale height is greater than that of a nondissipating wave field. A simple zero mean wind model based on linear saturation theory is found to be inadequate in reproducing the seasonal characteristics of the observed wave variances. An alternative model based on critical layer filtering by a height dependent wind field can reproduce the observed semiannual oscillation in the wave variance given a specific source input.

A generalized mathematical scheme to analytically solve the atmospheric diffusion equation with dry deposition

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed and eddy diffusivities, and with a Robin-type boundary condition at the ground. Unlike published solutions of similar problems where complex or non-programmable (e.g., hypergeometric or Kummer) functions are obtained, the analytical solution proposed herein consists of two previously derived Green's functions (modified Bessel functions) expressed in an integral form that is amenable to numerical integration. In the case of invariant wind speed and turbulent eddies with height (i.e., Gaussian deposition plume), the solution reduces to an equivalent well-known heat conduction solution. The physical behavior represented by the Green's functions comprising the solution can be interpreted. This generalized scheme can be modified further to account for inversion effects or other meteorological conditions. The solution derived is useful for examining the accuracy and performance of sophisticated numerical dispersion models, and is particularly suitable for modeling the transport of pollutants undergoing strong surface adsorption or high depositional losses.

Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorption), or mixed boundary conditions, the solutions for a single source are comprised of three components: a source strength, a crosswind dispersion factor, and a vertical dispersion factor. The two dispersion factors together constitute a Green's function—the concentration response due to a unit disturbance (source). When the general point source Green's functions are derived for a bounded domain (inversion effect) with various boundary conditions and arbitrary power-law profiles for wind speed and eddy diffusivities, previously published equations are found to be simplified versions of this more general case. A methodology based on the superposition of Green's functions is proposed, which enables the estimation of ambient concentrations not only from a single source, but also from multiple point, line, or area releases.

Atmospheric diffusion of small instantaneous point releases near the ground

The atmospheric dispersion of material released by a pulsed point source near the ground is discussed in the context of K theory. Approximate solutions to the diffusion equation, taking into account the effects of height-dependent wind velocity and turbulent diffusivities in the planetary boundary layer, are obtained by the method of moments. The approach is validated by comparing the predicted time/space dependent optical properties of obscurant clouds with experimental observations of explosion generated dust clouds. Parametric solutions, which exhibit the dependence of cloud history upon atmospheric stratification (stability category), are compared among themselves as well as with the predictions of classical Gaussian models. The cloud structures indicated by the present results for large (dimensionless) times differ markedly from those suggested by the Gaussian model. The cause of the divergence is determined, and the conditions where the Gaussian approximation may be retained are identified accordingly.

Bifurcation and Stability in a Model of Moist Convection in a Shearing Environment

The six-coefficient spectral model (model I) of two-dimensional shallow moist convection discussed by Shirer and Dutton (1979) is extended to an eleven component system (model II) in order that a height-dependent basic wind V(z) could be added to the problem. In this way, some behavior of atmospheric cloud streets that are usually observed in a shearing environment could be studied qualitatively. In model II, several different types of solutions exist that correspond to a rich variety of physically relevant possibilities. When a basic wind field is present, stationary, advecting or growing and decaying but propagating cloud bands may occur for different magnitudes of the vertical temperature gradient. These two-dimensional rolls are represented by time-dependent or periodic solutions or by an attractor on a two-dimensional torus. At large values of the lapse rate, the invariant set is probably contained on a three-dimensional torus, but whether or not the limit set is composed of a strange attractor (that may be a model of turbulent behavior) is an open question. With use of a minimizing principle, the expected cloud band orientations are obtained. The resulting formulas provide predictions that generally agree with the linear studies of previous investigators, but our equations apply to an arbitrary height-dependent wind field. When the wind direction does not vary with altitude, the branching two-dimensional rolls are longitudinal or aligned parallel to the wind shear vector. But when the basic wind direction changes with height, some wind profiles support longitudinal rolls; other wind fields load to transverse rolls that are oriented perpendicular to the shear. Two or three coexisting cloud band alignments can also occur.

Refraction of infrasound by upper-atmospheric winds

We used realistic models of upper-atmospheric winds in a three-dimensional acoustic ray-tracing program to calculate how much wind refraction alters acoustic transit speed and azimuth of arrival for long-distance paths. Transit speed varied by 20% or more, and bearing deviations of up to ten degrees were found, depending on the season and on the direction the waves travel. On the average, the predicted seasonal trends corresponded to osbervations, but the calculated standard deviations exceed the mean seasonal values, making simple corrections useless in individual cases. Furthermore, it is doubtful that variations of horizontally uniform winds alone can account for the large observed variability in refractive effects, specifically the large differences in bearing error at adjacent observatories. We show that realistic horizontal gradients of either temperature or wind could cause as much azimuthal refraction as our height-dependent wind models.