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NASA NTRS1980

The structure of correlation tensors in homogeneous anisotropic turbulence

The study of turbulence with spatially homogeneous but anisotropic statistical properties has applications in space physics and laboratory plasma physics. The first step in the systematic study of such fluctuations is the elucidation of the kinematic properties of the relevant statistical objects, which are the correlation tensors. The theory of isotropic tensors, developed by Robertson, Chandrasekhar and others, is reviewed and extended to cover the general case of turbulence with a pseudo-vector preferred direction, without assuming mirror reflection invariance. Attention is focused on two point correlation functions and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. It is also shown that the vector and pseudo-vector preferred direction cases yield different results. An explicit form of the two point correlation tensor is presented which is appropriate for analyzing interplanetary magnetic fluctuations. A procedure for determining the magnetic helicity from experimental data is presented.

Matthaeus, W. H.↗

NASA NTRS1993

Solar Nebula Magnetohydrodynamic Dynamos: Kinematic Theory, Dynamical Constraints, and Magnetic Transport of Angular Momentum

A hydromagnetic dynamo provides the best mechanism for contemporaneously producing magnetic fields in a turbulent solar nebula. We investigate the solar nebula in the framework of a steady-state accretion disk model and establish the criteria for a viable nebular dynamo. We have found that typically a magnetic gap exists in the nebula, the region where the degree of ionization is too small for the magnetic field to couple to the gas. The location and width of this gap depend on the particular model; the supposition is that gaps cover different parts of the nebula at different evolutionary stages. We have found, from several dynamical constraints, that the generated magnetic field is likely to saturate at a strength equal to equipartition with the kinetic energy of turbulence. Maxwell stress arising from a large-scale magnetic field may significantly influence nebular structure, and Maxwell stress due to small-scale fields can actually dominate other stresses in the inner parts of the nebula. We also argue that the bulk of nebular gas, within the scale height from the midplane, is stable against Balbus-Hawley instability.

Stepinski, Tomasz F.↗

NASA NTRS1994

Kinematic structure of the 30 Doradus giant H II region

We have used the echelle CCD spectrograph on the Cerro Tololo Inter-American Observatory (CTIO) 4 m telescope to map the nebular velocity field in the 30 Doradus giant H II region. The kinematics of 30 Dor are very complex. The outer regions are charaterized by a smooth velocity field, but its turbulent velocity, 30-40 km/s Full Width Half Maximum (FWHM), is considerably higher than those in most smaller H II regions. In the central 9 min core, multiple velocity components are observed at most positions. The velocity field is dominated by a large number of expanding structures, ranging in size from 1 to 100 pc and expansion velocities of 20-200 km/s, and often organized into large hierarchical networks. The integral of these complex expanding structures in 30 Dor produces a surprisingly simple profile with a broad Gaussian core and faint extended wings. Several fast-expanding shells, with diameters of 2-20 pc, expansion velocities of 100-300 km/s, and kinetic energies of 0.5-10 x 10(exp 50) ergs have been identified. The large fast-expanding shells and networks are coincident with extended X-ray sources and are probably associated with supernova remnants embedded in supershells produced by the combined effects of stellar winds and supernovae from OB associations. We have used the intensity-calibrated echelle spectra to determine the basic physical and dynamical properties of the kinematic features in 30 Dor. The expanding shells contain roughly half of the kinetic energy in the 30 Dor complex, and this energy is several times higher than the gravitational binding energy of the region. The energetic requirements of the gas are consistent with the observed stellar content of 30 Dor, if the gas is accelerated by a combination of stellar winds and supernovae. Extrapolating the current energy injection rate in the nebula over the lifetime of the OB complex suggest that 30 Dor and its vicinity will evolve into a supergiant shell as seen in the LMC and other nearby galaxies.

Chu, You-Hua↗

NASA NTRS1977

Turbulence Measurement in Transonic Flow

Two instrumentation systems are presently practical to use in turbulence measurements. The laser velocimeter can measure fluctuating velocities while the hot-wire anemometer, in principle, can be used to obtain both kinematic and thermodynamic fluctuations. In addition, the hot-wire anemometer gives an analog signal output that is convenient for use in time-space correlation studies and spectral analyses. The laser velocimeter has been used successfully in all flow regimes, whereas the hot wire has not been exploited in transonic flows, where the wire response has not been well-understood. The purpose of this Note is to examine the response and calibration of a constant-temperature, hot- wire anemometer in transonic flow and to present turbulence measurements, obtained in a transonic boundary layer.

Rose, William C.↗

NASA NTRS1950

Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction

Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.

BOUNDARY LAYER - WIND TUNNEL WALLS↗

NASA NTRS1995

GHRS observations of cool, low-gravity star. 2: Flow and turbulent velocities in the outer atmosphere of gamma CRU CIS (M3.4 III)

The Goddard High Resoulution Spectrograph (GHRS) on the Hubble Space Telescope (HST) has been used to obtain medium (R = 20,000) and high (R = 85,000) resoultion UV spectra of chromosphere emission features for the M3.4 III star gamma Cru. Small Science Aperture (SSA) G270M and Echelle-B spectra of selected regions in the 2300-2850 A range were obtained to determine the kinematics of the chromosphere using lines of C2), Fe2, Co2, Si1/2), Ni2, Mn2, and Mg2. Profiles of C2) (UV 0.01) lines and fluorescently excited lines of low optical depth indicate average turbulent velocities (Doppler FWHM) of 30.2 +/- 1.3 and 28.8 +/- 1.3 km/s, respectively. The fluorescent emission lines (mean RV = 21.3 +/- 0.9 km/s) and the wings of the emission components of Fe2 lines (mean RV = 22.8 +/- 0.4 km/s) are approximately at rest relative to the radial velocity of the star (21 km/s), while the C2) lines show a modest inflow (mean RV = 23.1 +/- 0.9 km/s). The more opaque lines of Fe2 and Mg2 exhibit complex profiles resulting from line formation in an optically thick, extended expanding atmosphere. The emission wings of these lines are broadened by multiple scattering, and they are centered near the photospheric radial velocity. Closer to line center, these strong lines show a strong blueshifted self-absorption feature (already seen in IUE data), indicative of formation in an expanding chromosphere, and a previously unseen dip in the profiles on the red side of line center. The absorption components, when extracted using simple Gaussian fits, show strong correlations with the relative optical depths of the lines. The derived absorption flow velocities converge to the photospheric velocity as one examines spectra features formed deeper in the atmosphere. The blueward abosrption velocity increases in magnitude from about 7 to 14 km/s with increasing line optical depth - the strong absorptions directly map the acceleration of the outflowing stellar wind, while the interpretation of the weaker redshifted abosrptions is more ambiguous, indicating either an inflow of material or formation in an extended, spherically expanding outflow. The Mg2 and Fe2 profiles, taken together, imply that the wind speed decreases between the atmospheric layers where the Mg2 and Fe2 self-absorption components are formed. Interstellar absorptions are seen in the resonance lines of Mg2 (UV 1) and Fe2 (UV1) with zero-volt lower levels, at about -3 km/s, consistent with models of the interstellar medium in the direction of gamma Cru. Finally, we have detected the Mg2 'satellite lines' seen in solar spectra obtained above the limb. In gamma Cru these lines are probably fluorescently excited by H Ly beta.

Carpenter, Kenneth G.↗

NASA NTRS1989

Large eddy simulation of the flow in a transpired channel

The flow in a transpired channel has been computed by large eddy simulation. The numerical results compare very well with experimental data. Blowing decreases the wall shear stress and enhances turbulent fluctuations, while suction has the opposite effect. The wall layer thickness normalized by the local wall shear velocity and kinematic viscosity increases on the blowing side of the channel and decreases on the suction side. Suction causes more rapid decay of the spectra, larger mean streak spacing and higher two-point correlations. On the blowing side, the wall layer structures lie at a steeper angle to the wall, whereas on the suction side this angle is shallower.

Piomelli, Ugo↗

NASA NTRS1983

The kinematics and structure of N63A and associated H II regions

Shull (1983) and Shull et al. (1982) discussed very high resolution spectrographic observations of bright knots in the filaments of the Cygnus Loop, IC 443, Puppis A, and Vela X supernova remnants (SNRs). Information on the small-scale thermal, turbulent, and bulk radial motions of the gas in these galactic remnants was obtained on the basis of an analysis of the spectral-line profiles. An analysis by Shull (1983) of N49, located in the Large Magellanic Cloud (LMC) is concerned with the large-scale structural and kinematic properties of N49 as it evolves in a cloudy interstellar medium (ISM). The present investigation represents the companion analysis of N63A, which is also a Type II SNR in the LMC. Echelle spectrograph observations indicate, for the first time, the large-scale kinematic and structural properties of the N63A system. They show clearly that the SNR, like N49, is evolving in a clumpy ISM.

Shull, P., Jr.↗

NASA NTRS2012

Broadband Noise Prediction When Turbulence Simulation Is Available - Derivation of Formulation 2B and Its Statistical Analysis

We show that a simple modification of Formulation 1 of Farassat results in a new analytic expression that is highly suitable for broadband noise prediction when extensive turbulence simulation is available. This result satisfies all the stringent requirements, such as permitting the use of the exact geometry and kinematics of the moving body, that we have set as our goal in the derivation of useful acoustic formulas for the prediction of rotating blade and airframe noise. We also derive a simple analytic expression for the autocorrelation of the acoustic pressure that is valid in the near and far fields. Our analysis is based on the time integral of the acoustic pressure that can easily be obtained at any resolution for any observer time interval and digitally analyzed for broadband noise prediction. We have named this result as Formulation 2B of Farassat. One significant consequence of Formulation 2B is the derivation of the acoustic velocity potential for the thickness and loading terms of the Ffowcs Williams-Hawkings (FW-H) equation. This will greatly enhance the usefulness of the Fast Scattering Code (FSC) by providing a high fidelity boundary condition input for scattering predictions.

Farassat, Fereidoun↗

NASA NTRS1975

A Standard Kinematic Model for Flight Simulation at NASA Ames

A standard kinematic model for aircraft simulation exists at NASA-Ames on a variety of computer systems, one of which is used to control the flight simulator for advanced aircraft (FSAA). The derivation of the kinematic model is given and various mathematical relationships are presented as a guide. These include descriptions of standardized simulation subsystems such as the atmospheric turbulence model and the generalized six-degrees-of-freedom trim routine, as well as an introduction to the emulative batch-processing system which enables this facility to optimize its real-time environment.

Mcfarland, R. E.↗

NASA NTRS1987

Third and higher harmonic plasma emission due to Raman scattering

The theory for third and higher harmonic plasma emission by the weak turbulence (or random phase) process L + T prime to T (where L denotes a Langmuir wave, and T and T prime denote transverse waves) is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes are identified. The cases of L waves produced either directly by a streaming instability, or by the decay L to L prime + S (S is an ion sound wave) of L waves generated by a streaming instability, are considered. Limits on the brightness temperature of the radiation are determined, and expressions for the growth rate and path-integrated wave temperatures are derived.

Cairns, Iver H.↗

NASA NTRS1979

Spray combustion models - A review

Due to recent theoretical and experimental advances, modeling spray combustion can be contemplated as a means of supplementing traditional cut and try combustor development methods. This review describes spray models that are currently being developed and their validation. The review is limited to steady, turbulent two- and three-dimensional systems typified by furnaces and gas turbine combustors. Both locally homogeneous flow models, where the phases are assumed to be in kinematic and thermodynamic equilibrium at each point in the flow, and more complete two-phase flow models, which allow for finite rate processes between the phases, are considered.

Faeth, G. M.↗

NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗

NASA NTRS1975

Turbulent flow between a rotating disk and a parallel wall

A scalar effective viscosity method is used to calculate the incompressible flow in the gap between two infinite, parallel smooth disks, one of them rotating and the other stationary. The flow is calculated for two values of the gap Reynolds number omega(s squared)/nu, namely 296 and 2852, where omega is the disk angular velocity, s the gap width, and nu the kinematic viscosity of the fluid; and over a range of radial Reynolds number omega(r squared)/nu from 0 to 10 million, where r is the radius from the axis of rotation. A numerical shooting technique is used to match the two boundary-layer flows arising on the disk and wall. Gradual transition is assumed for radial Reynolds numbers from 160,000 to 250,000. The results are in good agreement with Daily and Nece's measurements of velocity profiles and disk friction drag for enclosed rotating disks, and at sufficiently large radius the local skin friction approaches that of turbulent Couette flow.

Cooper, P.↗

NASA NTRS1973

Comments on the reconnexion rate of magnetic fields.

The reconnection rate of magnetic fields is crucial in understanding the fields found in turbulent flows in the solar photosphere and in the galaxy, and in flare phenomena. The behavior of magnetic fields in the neighborhood of an X-type neutral point is examined. The treatment is kinematic specifying the velocity field v and constructing solutions to the hydromagnetic equation for B. The calculations demonstrate that the reconnection rate is controlled by the diffusion in the near neighborhood of the neutral point, and is not arbitrarily large, as has been suggested by similarity solutions of the complete field and fluid equations for vanishing diffusion.

Parker, E. N.↗

NASA NTRS1977

A spin-orbit constraint on the viscosity of a Mercurian liquid core

The escape of Mercury from the stable spin-orbit resonance in which the spin angular velocity is twice the orbital mean motion (2n) requires that the kinematic viscosity of a molten core with a laminar boundary layer be comparable to that of water (0.01 sq cm/s) and the tidal Q be less than about 100. If the boundary layer is turbulent, escape from the resonance is only consistent with a liquid core of low viscosity if the critical Reynolds number for the onset of turbulence is above about 500, the moment difference (B - A)/C is below about 0.00001, and the tidal dissipation factor Q is less than about 40. These conclusions depend on the assumptions that Mercury's obliquity was near 0 deg at the time of resonance passage, that the liquid core was not stably stratified at the time at which Mercury passed through the resonance, that a turbulent boundary layer can be characterized by a turbulent or eddy viscosity coefficient, and that the most important coupling between core and mantle is a viscous coupling at a smooth spherical boundary.

Peale, S. J.↗

NASA NTRS1991

State estimation applications in aircraft flight-data analysis: A user's manual for SMACK

The evolution in the use of state estimation is traced for the analysis of aircraft flight data. A unifying mathematical framework for state estimation is reviewed, and several examples are presented that illustrate a general approach for checking instrument accuracy and data consistency, and for estimating variables that are difficult to measure. Recent applications associated with research aircraft flight tests and airline turbulence upsets are described. A computer program for aircraft state estimation is discussed in some detail. This document is intended to serve as a user's manual for the program called SMACK (SMoothing for AirCraft Kinematics). The diversity of the applications described emphasizes the potential advantages in using SMACK for flight-data analysis.

Bach, Ralph E., Jr.↗

NASA NTRS1991

A new solar cycle model including meridional circulation

A kinematic model is presented for the solar cycle which includes not only the transport of magnetic flux by supergranular diffusion and a poleward bulk flow at the sun's surface, but also the effects of turbulent diffusion and an equatorward 'return flow' beneath the surface. As in the earlier models of Babcock and Leighton, the rotational shearing of a subsurface poloidal field generates toroidal flux that erupts at the surface in the form of bipolar magnetic regions. However, such eruptions do not result in any net loss of toroidal flux from the sun (as assumed by Babcock and Leighton); instead, the large-scale toroidal field is destroyed both by 'unwinding' as the local poloidal field reverses its polarity, and by diffusion as the toroidal flux is transported equatorward by the subsurface flow and merged with its opposite hemisphere counterpart. The inclusion of meridional circulation allows stable oscillations of the magnetic field, accompanied by the equatorward progression of flux eruptions, to be achieved even in the absence of a radial gradient in the angular velocity. An illustrative case in which a subsurface flow speed of order 1 m/s and subsurface diffusion rate of order 10 sq km/s yield 22-yr oscillations in qualitative agreement with observations.

Wang, Y.-M.↗