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Equations are presented for calculating power law exponents from wind speed and surface roughness data. Results are evaluated by comparison with wind profile data measured at a variety of sites.
The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.
The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.
Traveling-wave bulk electroconvection induced in slightly conducting liquid with temperature gradient, giving velocity profile equations for plane flow
Method developed to account for effects of compressibility in viscous flows through long, circular pipes of uniform diameter. Based on approximation of variations in density and velocity across pipe cross section by profile equations developed for boundary-layer flow between flat plates.
The objectives were to apply energy balance principles to plant canopies, and to determine which parameters are essential for predicting plant canopy transpiration (E) in controlled environments. Transpiration was accurately measured in a gas-exchange system. Absorbed radiation (R(sub abs)) by the canopy was measured with a net radiometer and calculated from short and long-wave radiation components. Average canopy foliar temperature T(sub L) can be measured with an infrared radiometer, but since T(sub L) is seldom uniform, a weighed average measurement of T(sub L) must be made. The effective canopy temperature T(sub C) is that temperature that balances the energy flux between absorbed radiation and latent heat L(sub E) and sensible heat (H) fluxes. TC should exactly equal air temperature T(sub A) when L(sub E) equals R(sub abs). When unnecessary thermal radiation from the lighting system is removed by a water filter, the magnitude of L(sub E) from transpiration approaches Rabs and T(sub C) is close to T(sub A). Unlike field models, we included the energy used in photosynthesis and found that up to 10% of Rabs was used in photosynthesis. We calculated aerodynamic conductance for H from measurements of wind speed and canopy height using the wind profile equation. Canopy aerodynamic conductance ranged from.03 to.04 m/s for wind speeds from.6 to 1 m/s; thus a 0.1 C canopy to air temperature difference results in a sensible heat flux of about 4 W/sq m, which is only 1% of R(sub abs). We examined the ability of wide angle infrared transducers to accurately integrate T(sub L) from the top to the bottom of the canopy. We measured evaporation from the hydroponic media to be approximately 1 micro mol/sq m s or 10% of R(sub abs). This result indicates that separating evaporation from transpiration is more important than exact measurement of canopy temperature.
In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.
Calculating profiles of Stokes parameters and degrees of linear and circular polarization using narrow band birefringent filter
Differential equation for parent and daughter decay influence on radioactive tracer diffusion profiles
The E × B staircase is a quasi-periodic pattern of pressure profile corrugations. In this work, we present a new mechanism for E × B staircase formation that involves resonant transport versus non-resonant transport. We start from a potential vorticity evolution system and use quasi-linear theory, a model dispersion relation, and a bi-Lorentzian spectrum approximation, to construct the relation between the fluxes and the profiles. With these fluxes, we close the profile evolution equations and the extended turbulence intensity evolution equation, which together constitute a turbulence-profile evolution system. In this system, the Doppler effect from the E × B mean flow can cause resonance between trapped ion precession motion and the trapped ion mode, which drives a resonant transport contribution to the fluxes. The profiles will be flattened where the resonant transport is switched on. In contrast, for the regions of non-resonant transport, profiles are steeper. A quasi-periodic pattern of profile corrugation (the E × B staircase) spontaneously emerges in this system, which is the two states mentioned above, arranged as alternating layers in space. The feedback processes during the staircase pattern formation are identified. An estimate of the critical value of the boundary heat flux is obtained, above which the staircase formation will be triggered. An estimate scaling of the step size in the staircase pattern is obtained. The resonant turbulent transport is also a mechanism for collisionless saturation of zonal flow. Furthermore, this work is related to internal transport barrier formation and suggests some new scenarios, such as an enhanced confined L mode.
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Electron density profiles of E region in vicinity of geomagnetic equator measured by Nike-Apache rockets
A two-dimensional, nonreacting flow model of the aerodynamic interaction of a transverse hydrogen jet within a supersonic mainstream has been developed. The model assumes profile shapes of mass flux, pressure, flow angle, and hydrogen concentration and produces downstream profiles of the other flow parameters under the constraints of the integrated conservation equations. These profiles are used as starting conditions for an existing finite difference parabolic computer code for the turbulent supersonic combustion of hydrogen. Integrated mixing and flow profile results obtained from the computer code compare favorably with existing data for the supersonic combustion of hydrogen.
Daytime D region electron density profiles at magnetic equator from ARCAS flights
Differential equation of temperature profile in carbon zone of ablator simulated using digital- analog simulator language /MIMIC/
The structure of a cylindrical blast wave with ionization at non-LTE conditions was calculated using equations previously developed by Wu and Fu (1970). The degree of ionization was predicted by a modified Saha equation. Temperature profiles show that the temperature at non-LTE conditions is lower than at LTE near the shock front. This corresponds to a higher degree of ionization for the non-LTE limit, which indicates that the neutral gas absorption is much more efficient at non-LTE than at the LTE limit. The decaying velocity under non-LTE is approximately 15% less than under LTE.
This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures. These layers consist of two counterflowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemical- species masses. In these equations, the expressions for heat fluxes and chemical-species mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the errorfunction profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles
Generation of vertical temperatures profiles from remotely sensed atmospheric radiance data is described as an analogous communications system. The radiative transport characteristics of the atmosphere encodes the continuous temperature profile into an 'n' element vector where 'n' is the number of channels in the satellite instrument. The temperature profile is a message transmitted from station A to station B and the link is the satellite instrument. At station B the decoder reproduces a continuous function which is the best estimate of the message encoded at station A. It is shown that the decoder must operate in a tuned mode where the parameters used in the encoder precisely determine the decoder parameters, and that the characteristics of the total message block must be given by a set of decoder constraints