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- Author or Editor: C. G. Justus x
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Abstract
A theory for the three-dimensional energy spectrum of nearly isotropic shear-dependent turbulence is presented. This theory is based on the author's general model for shear-dependent turbulence and a modified Pao spectral transfer theory which accounts for the effects of viscous loss, shear production, and inertial and velocity gradient transfer in nonstationary turbulence. The resultant spectral transfer equation is solved in closed form for the case of complete similarity. The small wavenumber stationary energy spectrum is shown to vary as k 4. The small wavenumber nonstationary solution varies as k 6, where θ can have values from 1–4. One-dimensional spectra are computed numerically and compared with the turbulence spectra observed for wind tunnel turbulence with a wide range of Reynolds numbers. The theory successfully predicts several features of the observed spectra at both high and low wavenumbers as well as in the inertial region.
Abstract
A theory for the three-dimensional energy spectrum of nearly isotropic shear-dependent turbulence is presented. This theory is based on the author's general model for shear-dependent turbulence and a modified Pao spectral transfer theory which accounts for the effects of viscous loss, shear production, and inertial and velocity gradient transfer in nonstationary turbulence. The resultant spectral transfer equation is solved in closed form for the case of complete similarity. The small wavenumber stationary energy spectrum is shown to vary as k 4. The small wavenumber nonstationary solution varies as k 6, where θ can have values from 1–4. One-dimensional spectra are computed numerically and compared with the turbulence spectra observed for wind tunnel turbulence with a wide range of Reynolds numbers. The theory successfully predicts several features of the observed spectra at both high and low wavenumbers as well as in the inertial region.
Abstract
A review is given of some recent measurements of the following energy balance parameters in the 90–110 km height region: ε0, the viscous dissipation of kinetic energy by shears in the mean winds; ε d , the viscous dissipation of kinetic energy by shears in the turbulent winds; ε s , the transfer of kinetic energy from the mean motion to the turbulent motion; ε g , the transfer of turbulent kinetic energy to potential energy by buoyancy action; and ε w , the rate of dissipation of wave energy of tides and irregular winds interpreted as gravity waves. Some measurements of the growth rates of globular structure on chemical release clouds and the growth rate of interglobular distances are presented. These data indicate that the diffusion mechanism is a mixture of the 〈v 2〉t 2 variation expected for the diffusion of a point from its initial position with the ε dt 3 variation expected for the variation of the separation between pairs of points.
Abstract
A review is given of some recent measurements of the following energy balance parameters in the 90–110 km height region: ε0, the viscous dissipation of kinetic energy by shears in the mean winds; ε d , the viscous dissipation of kinetic energy by shears in the turbulent winds; ε s , the transfer of kinetic energy from the mean motion to the turbulent motion; ε g , the transfer of turbulent kinetic energy to potential energy by buoyancy action; and ε w , the rate of dissipation of wave energy of tides and irregular winds interpreted as gravity waves. Some measurements of the growth rates of globular structure on chemical release clouds and the growth rate of interglobular distances are presented. These data indicate that the diffusion mechanism is a mixture of the 〈v 2〉t 2 variation expected for the diffusion of a point from its initial position with the ε dt 3 variation expected for the variation of the separation between pairs of points.
Abstract
Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analysed by a daily-difference method, and results on the magnitude of atmospheric perturbations interpreted as gravity waves and planetary waves are presented. Traveling planetary-wave contributions in the 25–85 km range were found to have a significant height and latitudinal variation. It was found that observed gravity-wave density perturbations and wind are related to one another in the manner predicted by gravity-wave theory. It was determined that, on the average, gravity-wave energy deposition or reflection occurs at all altitudes except the 55–75 km region of the mesosphere.
Abstract
Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analysed by a daily-difference method, and results on the magnitude of atmospheric perturbations interpreted as gravity waves and planetary waves are presented. Traveling planetary-wave contributions in the 25–85 km range were found to have a significant height and latitudinal variation. It was found that observed gravity-wave density perturbations and wind are related to one another in the manner predicted by gravity-wave theory. It was determined that, on the average, gravity-wave energy deposition or reflection occurs at all altitudes except the 55–75 km region of the mesosphere.
Abstract
A simple model is presented that, in a cloud-free atmosphere, calculates solar spectral direct and diffuse irradiance and directional radiance at the surface, spectral absorption within the atmosphere and the upward reflected spectral irradiance or directional radiance at the top of the atmosphere. The irradiance model, based on similar approaches by Brine and Iqbal and others, evaluates the spectral irradiances between 0.29 and 4.0 μm, with a resolution that varies from 0.005 to 0.1 μm. Absorption by water vapor, ozone and the uniformly mixed gases is included, as are both scattering and absorption by atmospheric aerosols, which are modeled with simple wavelength-dependent optical depth, single scattering albedo and asymmetry parameter functions. Comparisons are presented of the model results with spectral irradiance and radiance computed by other more sophisticated models and with measurements from both ground-based and satellite instruments. The reasonable accuracy and simplicity of the model make it suitable for a number of applications, especially those involving tests of the sensitivity of spectral irradiances or radiances to variations in water vapor, ozone and various aerosol parameters.
Abstract
A simple model is presented that, in a cloud-free atmosphere, calculates solar spectral direct and diffuse irradiance and directional radiance at the surface, spectral absorption within the atmosphere and the upward reflected spectral irradiance or directional radiance at the top of the atmosphere. The irradiance model, based on similar approaches by Brine and Iqbal and others, evaluates the spectral irradiances between 0.29 and 4.0 μm, with a resolution that varies from 0.005 to 0.1 μm. Absorption by water vapor, ozone and the uniformly mixed gases is included, as are both scattering and absorption by atmospheric aerosols, which are modeled with simple wavelength-dependent optical depth, single scattering albedo and asymmetry parameter functions. Comparisons are presented of the model results with spectral irradiance and radiance computed by other more sophisticated models and with measurements from both ground-based and satellite instruments. The reasonable accuracy and simplicity of the model make it suitable for a number of applications, especially those involving tests of the sensitivity of spectral irradiances or radiances to variations in water vapor, ozone and various aerosol parameters.
Abstract
A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of ∼10%–15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.
Abstract
A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of ∼10%–15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.
Abstract
Spatial cross correlations and interannual and month-to-month variations of monthly mean wind speed were studied at 40 sites throughout the United States. Sites were selected on the basis of availability of 10 or more years of data from a fixed anemometer location and height and a climatological mean speed of 5 m s−1 (11 mph) or higher. Spatial cross correlations of monthly deviations from climatic means were found to be about 0.5 for sites separated less than 200 km, with annual mean wind deviations from the climatic mean correlated with coefficient value 0.32 for similarly separated sites. Applications for using nearby “climatological” site wind speed data to adjust short-term “candidate” site data are examined with several methods. The best results show only minimal improvement in estimating the long-term annual mean over that obtained from one year of on-site data. These results indicate that, for candidate wind energy site evaluation, on-site data must be relied on more than originally considered and climatological data relied on less. Probability distributions of monthly and annual mean speeds were found to be nearly Gaussian with respect to climatological montly or annual mean. These distributions were found to have median (50 percentile) values of V/V=0.99, with coefficients of variation σ/V ranging from 0.08 to 0.18 (average 0.11) for monthly means and from 0.03–0.12 (0.06 average) for annual means. The coefficients of variation were found to be independent of climatic mean speed V, and the median V/V and σ/V values for a given site were found to be independent of season. Time autocorrelations were found to be about 0.33 for monthly mean speed with one-month lag and for annual mean speed with one-year lag. This corresponds to a persistence probability (probability of deviation from climatic mean retaining the same sign over one time lag) of about 63%.
Abstract
Spatial cross correlations and interannual and month-to-month variations of monthly mean wind speed were studied at 40 sites throughout the United States. Sites were selected on the basis of availability of 10 or more years of data from a fixed anemometer location and height and a climatological mean speed of 5 m s−1 (11 mph) or higher. Spatial cross correlations of monthly deviations from climatic means were found to be about 0.5 for sites separated less than 200 km, with annual mean wind deviations from the climatic mean correlated with coefficient value 0.32 for similarly separated sites. Applications for using nearby “climatological” site wind speed data to adjust short-term “candidate” site data are examined with several methods. The best results show only minimal improvement in estimating the long-term annual mean over that obtained from one year of on-site data. These results indicate that, for candidate wind energy site evaluation, on-site data must be relied on more than originally considered and climatological data relied on less. Probability distributions of monthly and annual mean speeds were found to be nearly Gaussian with respect to climatological montly or annual mean. These distributions were found to have median (50 percentile) values of V/V=0.99, with coefficients of variation σ/V ranging from 0.08 to 0.18 (average 0.11) for monthly means and from 0.03–0.12 (0.06 average) for annual means. The coefficients of variation were found to be independent of climatic mean speed V, and the median V/V and σ/V values for a given site were found to be independent of season. Time autocorrelations were found to be about 0.33 for monthly mean speed with one-month lag and for annual mean speed with one-year lag. This corresponds to a persistence probability (probability of deviation from climatic mean retaining the same sign over one time lag) of about 63%.
Abstract
The Weibull function is discussed for representation of the wind speed frequency distribution. Methods are presented for estimating the two Weibull parameters (scale factor c and shape factor k) from simple wind statistics. Comparison is made with a recently proposed method based on the “square-root-normal” distribution with mean wind speed and fastest mile data as input statistics. The Weibull distribution is shown to give smaller root-mean-square errors than the square-root-normal distribution when fitting actual distributions of observed wind speed. Another advantage of the Weibull distribution is the available methodology for projecting to another height the observed Weibull distribution parameters at anemometer height.
Abstract
The Weibull function is discussed for representation of the wind speed frequency distribution. Methods are presented for estimating the two Weibull parameters (scale factor c and shape factor k) from simple wind statistics. Comparison is made with a recently proposed method based on the “square-root-normal” distribution with mean wind speed and fastest mile data as input statistics. The Weibull distribution is shown to give smaller root-mean-square errors than the square-root-normal distribution when fitting actual distributions of observed wind speed. Another advantage of the Weibull distribution is the available methodology for projecting to another height the observed Weibull distribution parameters at anemometer height.
Abstract
A method of computing power output from wind-powered generators has been developed and applied to estimate potential power output at various sites across the continental United States. The method assumes a wind-powered generator system which can be characterized by a cut-in speed V 0, a rated speed V 1 and a cut-out speed V 2. The generator output power is assumed to be constant at the rated power Pr between V 1 and V 2 and to vary parabolically from zero at V 0 to Pr at V 1. The wind distributions at various sites have been found to vary according to a Weibull distribution between realistic values of V 0 and V 1. Values of the Weibull distribution parameters at approximately 135 sites across the United States have been evaluated. These results have been projected to a constant height of 30.5 m (100 ft) and 61 m (200 ft) using data determined from observed Weibull parameter height variations at several meteorological tower sites across the country. A contour map is presented for generator capacity factor values (fraction of rated power output actually realizable). The capacity factor values were computed, using the above method, for wind-powered generator systems having cut-in speed V 0 = 3.6 m s−1(8 mph), and rated speed V 1 = 8.0 m s−1 (18 mph), the characteristics of NASA's 100 kW Plumbrook unit, and V 0 = 6.7 m s−1 (15 mph), V 1 = 13.4 m s−1 (30 mph), hypothetical values for a 1 MW class unit. Results of the evaluation indicate that at a height of 61 m in the central United States and in certain portions of the New England coast over 60% of rated output power can be achieved on an annual average basis, i.e., an average of ≥60 kW from the Plumbrook 100 kW generator. In these same areas the 1 MW system would have over 20% capacity factors, i.e., an average of ≥200 kW from the 1 MW system.
Abstract
A method of computing power output from wind-powered generators has been developed and applied to estimate potential power output at various sites across the continental United States. The method assumes a wind-powered generator system which can be characterized by a cut-in speed V 0, a rated speed V 1 and a cut-out speed V 2. The generator output power is assumed to be constant at the rated power Pr between V 1 and V 2 and to vary parabolically from zero at V 0 to Pr at V 1. The wind distributions at various sites have been found to vary according to a Weibull distribution between realistic values of V 0 and V 1. Values of the Weibull distribution parameters at approximately 135 sites across the United States have been evaluated. These results have been projected to a constant height of 30.5 m (100 ft) and 61 m (200 ft) using data determined from observed Weibull parameter height variations at several meteorological tower sites across the country. A contour map is presented for generator capacity factor values (fraction of rated power output actually realizable). The capacity factor values were computed, using the above method, for wind-powered generator systems having cut-in speed V 0 = 3.6 m s−1(8 mph), and rated speed V 1 = 8.0 m s−1 (18 mph), the characteristics of NASA's 100 kW Plumbrook unit, and V 0 = 6.7 m s−1 (15 mph), V 1 = 13.4 m s−1 (30 mph), hypothetical values for a 1 MW class unit. Results of the evaluation indicate that at a height of 61 m in the central United States and in certain portions of the New England coast over 60% of rated output power can be achieved on an annual average basis, i.e., an average of ≥60 kW from the Plumbrook 100 kW generator. In these same areas the 1 MW system would have over 20% capacity factors, i.e., an average of ≥200 kW from the 1 MW system.
Abstract
An empirical atmospheric model has been developed which generates values for pressure, density, temperature and winds from surface levels to orbital altitudes. The output parameters consist of components for: 1) latitude, longitude, and altitude dependent monthly means; 2) quasibiennial oscillations; and 3) random perturbations to partially simulate the variability due to synoptic, diurnal, planetary wave and gravity wave variations. The monthly mean models consist of: (i) NASA's four dimensional worldwide model, developed by Environmental Research and Technology, for height, latitude, and longitude dependent monthly means from the surface to 25 km; and (ii) a newly developed latitude-longitude dependent model which is an extension of the Groves latitude dependent model for the region between 25 and 90 km. The Jacchia 1970 model is used above 90 km and is faired with the modified Groves values between 90 and 115 km. Quasibiennial and random variation perturbations are computed from parameters determined from various empirical studies, and are added to the monthly mean values. This model has been developed as a computer program which can be used to generate altitude profiles of atmospheric variables for any month at any desired location, or to evaluate atmospheric parameters along any simulated trajectory through the atmosphere. Various applications of the model are discussed, and results are presented which show that good simulation of the thermodynamic and circulation characteristics of the atmosphere can be achieved with the model.
Abstract
An empirical atmospheric model has been developed which generates values for pressure, density, temperature and winds from surface levels to orbital altitudes. The output parameters consist of components for: 1) latitude, longitude, and altitude dependent monthly means; 2) quasibiennial oscillations; and 3) random perturbations to partially simulate the variability due to synoptic, diurnal, planetary wave and gravity wave variations. The monthly mean models consist of: (i) NASA's four dimensional worldwide model, developed by Environmental Research and Technology, for height, latitude, and longitude dependent monthly means from the surface to 25 km; and (ii) a newly developed latitude-longitude dependent model which is an extension of the Groves latitude dependent model for the region between 25 and 90 km. The Jacchia 1970 model is used above 90 km and is faired with the modified Groves values between 90 and 115 km. Quasibiennial and random variation perturbations are computed from parameters determined from various empirical studies, and are added to the monthly mean values. This model has been developed as a computer program which can be used to generate altitude profiles of atmospheric variables for any month at any desired location, or to evaluate atmospheric parameters along any simulated trajectory through the atmosphere. Various applications of the model are discussed, and results are presented which show that good simulation of the thermodynamic and circulation characteristics of the atmosphere can be achieved with the model.
