Passive Scalar Transport by Random Waves
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equation mean concentration field↗
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The solution of the laminar-boundary-layer equation for the flat plate for velocity and temperature fields for variable physical properties and for the diffusion field at high concentration
In connection with Pohlhausen's solution for the temperature field on the flat plate, a series of formulas were indicated by means of which the velocity and temperature field for variable physical characteristics can be computed by an integral equation and an iteration method based on it. With it, the following cases were solved: On the assumption that the viscosity simply varies with the temperature while the other fluid properties remain constant, the velocity and temperature field on the heated and cooled plate, respectively, was computed at the Prandtl numbers 12.5 and 100 (viscous fluids). A closer study of these two cases resulted in general relations: The calculations for a gas of Pr number 0.7 (air) were conducted on the assumption that all fluid properties vary with the temperature, and the velocities are low enough for the heat of friction to be discounted. The result was a thickening of the boundary layers, but no appreciable modification in shearing stress or heat-transfer coefficient.
BOUNDARY LAYER, LAMINAR - PLATES, FLAT↗
Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration
Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, this technique is extended to mass points and mass disks in the gravity field. This requires the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.
Ananda, M.↗
Turbulent shear flow of continuum plasma.
The turbulence structure of weakly ionized, continuum plasma is analyzed with emphasis on the turbulent fluctuation and the transport properties of the ionized species. The mean gradients of the velocity and ionized-species concentrations are considered to be uniform. It is assumed that the turbulence Reynolds number is small and that the turbulence field is homogeneous in order to close the dynamic equations of turbulence. It was found that the ratio of the Debye shielding length to the local integral scale of turbulence must be sufficiently small in order for the detailed quasi-neutrality to prevail. The condition of the detailed quasi-neutrality is necessary, in addition to the equal mean concentrations of electrons and ions, in order for the turbulence properties involving the electrons to be the same as those involving the ions.
Chung, P. M.↗
QES-Plume v1.0: a Lagrangian dispersion model
Low-cost simulations providing accurate predictions of transport of airborne material in urban areas, vegetative canopies, and complex terrain are demanding because of the small-scale heterogeneity of the features influencing the mean flow and turbulence fields. Common models used to predict turbulent transport of passive scalars are based on the Lagrangian stochastic dispersion model. The Quick Environmental Simulation (QES) tool is a low-computational-cost framework developed to provide high-resolution wind and concentration fields in a variety of complex atmospheric-boundary-layer environments. Part of the framework, QES-Plume, is a Lagrangian dispersion code that uses a time-implicit integration scheme to solve the generalized Langevin equations which require mean flow and turbulence fields. Here, QES-Plume is driven by QES-Winds, a 3D fast-response model that computes mass-consistent wind fields around buildings, vegetation, and hills using empirical parameterizations, and QES-Turb, a local-mixing-length turbulence model. In this paper, the particle dispersion model is presented and validated against analytical solutions to examine QES-Plume’s performance under idealized conditions. In particular, QES-Plume is evaluated against a classical Gaussian plume model for an elevated continuous point-source release in uniform flow, the Lagrangian scaling of dispersion in isotropic turbulence, and a non-Gaussian plume model for an elevated continuous point-source release in a power-law boundary-layer flow. In these cases, QES-Plume yields a maximum relative error below 6 % when compared with analytical solutions. In addition, the model is tested against wind-tunnel data for a uniform array of cubical buildings. QES-Plume exhibits good agreement with the experiment with 99 % of matched zeros and 59 % of the predicted concentrations falling within a factor of 2 of the experimental concentrations. Furthermore, results also emphasize the importance of using high-quality turbulence models for particle dispersion in complex environments. Finally, QES-Plume demonstrates excellent computational performance.
58 GEOSCIENCES↗
Estimation of atmospheric species concentrations from remote sensing data
The atmospheric species concentration distribution-estimation problem that arises from the measurement configuration of remote sensing, which involves a field of view that moves across the region, is solved by means of the partial differential equation for atmospheric diffusion and the Wiener-Hopf theory. A numerical study is also undertaken for the estimation of concentration distribution downwind of a hypothetical, continuous ground-level source of pollutants.
Omatu, S.↗
Suppression of nonlinear oscillations in combustors with partial length acoustic liners
An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.
Espander, W. R.↗
The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field
The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.
Kulsrud, Russell M.↗
Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows
Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.
Hogan, Robert C.↗
Modelling of jet- and swirl-stabilized reacting flows in axisymmetric combustors
Turbulent nonreactive and reactive flows with and without swirl are analyzed, with particular attention given to the flow fields of a gas-fueled nonpremixed swirl-stabilized combustor and a premixed opposed-jet combustor. Local mean flow properties, including velocity, temperature, and major species concentrations, are calculated by solving numerically the governing partial differential equations with associated submodels for turbulence and combustion. The results of the study indicate that the constant-density k-epsilon turbulence model provides a satisfactory representation of the aerodynamics in most practical combustor flows. The exception is the case of jet-stabilized combustor flow, due to the fact that the k-epsilon model cannot replicate the highly dissipative phenomenon found in such flows.
Nikjooy, M.↗
Titan's Atmospheric Dynamics and Meteorology
Titan, after Venus, is the second example of an atmosphere with a global cyclostrophic circulation in the solar system, but a circulation that has a strong seasonal modulation in the middle atmosphere. Direct measurement of Titan's winds, particularly observations tracking the Huygens probe at 10degS, indicate that the zonal winds are generally in the sense of the satellites rotation. They become cyclostrophic approx. 35 km above the surface and generally increase with altitude, with the exception of a sharp minimum centered near 75 km, where the wind velocity decreases to nearly zero. Zonal winds derived from the temperature field retrieved from Cassini measurements, using the thermal wind equation, indicate a strong winter circumpolar vortex, with maximum winds at mid northern latitudes of 190 ms-' near 300 km. Above this level, the vortex decays. Curiously, the zonal winds and temperatures are symmetric about a pole that is offset from the surface pole by approx.4 degrees. The cause of this is not well understood, but it may reflect the response of a cyclostrophic circulation to the offset between the equator, where the distance to the rotation axis is greatest, and the solar equator. The mean meridional circulation can be inferred from the temperature field and the meridional distribution of organic molecules and condensates and hazes. Both the warm temperatures in the north polar region near 400 km and the enhanced concentration of several organic molecules suggests subsidence there during winter and early spring. Stratospheric condensates are localized at high northern latitudes, with a sharp cut-off near 50degN. Titan's winter polar vortex appears to share many of the same characteristics of winter vortices on Earth-the ozone holes. Global mapping of temperatures, winds, and composition in he troposphere, by contrast, is incomplete. The few suitable discrete clouds that have bee found for tracking indicate smaller velocities than aloft, consistent with the Huygens measurements. At low latitudes the zonal winds near the surface appear not to be westward as on Earth, but eastward. Because the net zonal-mean time-averaged torq exerted by the surface on the atmosphere should vanish, this implies westward flow o part of the surface; the question is where. The latitude contrast in tropospheric temperatures, deduced from radio occultations at low, mid, and high latitudes, is small approx.5 K at the tropopause and approx.3 K at the surface.
Flasar, F. M.↗
Numerical analysis of confined turbulent flow
The considered investigation is concerned with the development of an efficient computational method for obtaining a physical understanding of an internal turbulent field. The employed approach makes use of a 'two equation' type model for the turbulence to obtain the numerical solution of a two-dimensional confined turbulent flow. The mean flow governing equations are considered along with the governing equation of the mean temperature and concentrations, and the boundary conditions. The numerical procedure for solving the turbulent flow is discussed, taking into account an approximation to the nonlinear terms, and the inner and outer coupling. Attention is given to a stability convergence analysis, the stability characteristics, and computational examples.
Lin, A.↗
Chapter 13. Atmospheric Dynamics and Meteorology
Titan, after Venus, is the second example in the solar system of an atmosphere with a global cyclostrophic circulation, but in this case a circulation that has a strong seasonal modulation in the middle atmosphere. Direct measurement of Titan's winds, particularly observations tracking the Huygens probe at 10 deg S, indicate that the zonal winds are mostly in the sense of the satellite's rotation. They generally increase with altitude and become cyclostrophic near 35 km above the surface. An exception to this is a sharp minimum centered near 75 km, where the wind velocity decreases to nearly zero. Zonal winds derived from temperatures retrieved from Cassini orbiter measurements, using the thermal wind equation, indicate a strong winter circumpolar vortex, with maximum winds of 190 m/s at mid northern latitudes near 300 km. Above this level, the vortex decays. Curiously, the stratospheric zonal winds and temperatures in both hemispheres are symmetric about a pole that is offset from the surface pole by about 4 deg. The cause of this is not well understood, but it may reflect the response of a cyclostrophic circulation to the onset between the equator, where the distance to the rotation axis is greatest, and the seasonally varying subsolar latitude. The mean meridional circulation can be inferred from the temperature field and the meridional distribution of organic molecules and condensates and hazes. Both the warm temperatures near 400 km and the enhanced concentration of several organic molecules suggest subsidence in the north polar region during winter and early spring. Stratospheric condensates are localized at high northern latitudes, with a sharp cut-off near 50 deg N. Titan's winter polar vortex appears to share many of the same characteristics of isolating high and low-latitude air masses as do the winter polar vortices on Earth that envelop the ozone holes. Global mapping of temperatures, winds, and composition in the troposphere, by contrast, is incomplete. The few suitable discrete clouds that have been found for tracking indicate smaller velocities than aloft, consistent: with the Huygens measurements, Along the descent trajectory, the Huygens measurements indicate eastward zonal winds down to 7 km, where they shift westward, and then eastward again below 1 km dawn to the surface. The low-latitude dune fields seen in Cassini RADAR images have been interpreted as longitudinal dunes occurring in a mean eastward zonal wind. This is not like Earth, where the low-latitude winds are westward above the surface. Because the net zonal-mean time-averaged torque exerted by the surface on the atmosphere should vanish, there must be westward flow over part of the surface; the question is where and when. The meridional contrast in tropospheric temperatures deduced from radio occultations at low, mid, and high latitudes. is small, approximately 5 K at the tropopause and approximately 3 K at the surface. This implies efficient heat transport, probably by axisymmetric meridional circulations. The effect of the methane "hydrological" cycle on the atmospheric circulation is not well constrained by existing measurements, Understanding the mature of the surface-atmosphere coupling will be critical to elucidating the atmospheric transports of momentum, heat, and volatiles.
Flasar, F. M.↗
Influence of airfoil nose radius on sound generated by gust interactions
The sound radiated by interaction of a short wavelength gust (k much greater than 1) with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. Airfoil thickness produces terms of relative order O(sq rt S) in the far field sound, where S is a Strouhal number based on the airfoil nose radius. At low Mach numbers, entropy gusts generate much less sound than vorticity gusts. However, for O(1) Mach numbers and moderate values of S, entropy and vorticity gusts produce similar sound levels.
Tsai, C. T.↗
A multiscale numerical study into the cascade of kinetic energy leading to severe local storms
The cascade of kinetic energy from macro- through mesoscales is studied on the basis of a nested grid system used to solve a set of nonlinear differential equations. The kinetic energy cascade and the concentration of vorticity through the hydrodynamic spectrum provide a means for predicting the location and intensity of severe weather from large-scale data sets. A mechanism described by the surface pressure tendency equation proves to be important in explaining how initial middle-tropospheric mass-momentum imbalances alter the low-level pressure field.
Paine, D. A.↗
Influence of airfoil thickness on sound generated by high-frequency gust interactions
The sound radiated by interaction of a short wavelength gust with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. At low Mach numbers, moderate values of airfoil thickness decrease the sound power, while at higher Mach numbers the sound power tends to increase with airfoil thickness. Airfoil thickness produces dramatic changes in the far field directivity. Both the sound power and the directivity are strong functions of the gust orientation.
Tsai, C. T.↗
The chemical composition of the dust-free Martian atmosphere - Preliminary results of a two-dimensional model
This paper describes a two-dimensional model of the Martian atmosphere, in which chemical, radiative and dynamical processes are treated interactively. The model is developed for a carbon dioxide-hydrogen-oxygen-nitrogen atmosphere and provides estimates of concentrations for 19 chemical species. The dynamical equations are expressed in the transformed Eulerian coordinates. The wave driving and eddy mixing coefficients resulting from gravity and Rossby wave absorption are computed consistently with the evolving distribution of the mean zonal wind. The net diabatic heating/cooling rate is derived from a detailed radiative scheme including the contributions of CO2, O3, H2O and O2, and is computed consistently with the calculated distribution of temperature and trace species quantities. The computed temperature field as well as the meridional and seasonal variations of ozone column abundance are in good agreement with the distributions observed by Mariner 9 and Viking spacecrafts and the results obtained by previous studies. The present version of the model does not include the effects of dust, clouds and polar hood and only the chemistry in a dust-free atmosphere is considered.
Moreau, D.↗
A model for reaction rates in turbulent reacting flows
To account for the turbulent temperature and species-concentration fluctuations, a model is presented on the effects of chemical reaction rates in computer analyses of turbulent reacting flows. The model results in two parameters which multiply the terms in the reaction-rate equations. For these two parameters, graphs are presented as functions of the mean values and intensity of the turbulent fluctuations of the temperature and species concentrations. These graphs will facilitate incorporation of the model into existing computer programs which describe turbulent reacting flows. When the model was used in a two-dimensional parabolic-flow computer code to predict the behavior of an experimental, supersonic hydrogen jet burning in air, some improvement in agreement with the experimental data was obtained in the far field in the region near the jet centerline. Recommendations are included for further improvement of the model and for additional comparisons with experimental data.
Chinitz, W.↗