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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electrostatic approximation

The plasma weak turbulence theory is a perturbative nonlinear theory, which has been proven to be quite valid in a number of applications. However, the standard weak turbulence theory found in the literature is fully developed for highly idealized unmagnetized plasmas. As many plasmas found in nature and laboratory are immersed in a background static magnetic field, it is necessary to extend the existing discussions to include the effects of ambient magnetic field. Such a task is quite formidable, however, which has prevented fundamental and significant progresses in the subject matter. The central difficulty lies in the formulation of the complete nonlinear response functions for magnetized plasmas. The present paper derives the nonlinear susceptibilities for weakly turbulent magnetized plasmas up to the third order nonlinearity, but in doing so, a substantial reduction in mathematical complexity is achieved by the use of Bessel function addition theorem (or sum rule). The present paper also constructs the weak turbulence wave kinetic equation in a formal sense. For the sake of simplicity, however, the present paper assumes the electrostatic interaction among plasma particles. Fully electromagnetic generalization is a subject of a subsequent paper.

Physics↗
DOE OSTI2020

3D turbulent reconnection: Theory, tests, and astrophysical implications

Magnetic reconnection, topological changes in magnetic fields, is a fundamental process in magnetized plasmas. It is associated with energy release in regions of magnetic field annihilation, but this is only one facet of this process. Astrophysical fluid flows normally have very large Reynolds numbers and are expected to be turbulent, in agreement with observations. In strong turbulence, magnetic field lines constantly reconnect everywhere and on all scales, thus making magnetic reconnection an intrinsic part of the turbulent cascade. We note in particular that this is inconsistent with the usual practice of magnetic field lines as persistent dynamical elements. A number of theoretical, numerical, and observational studies starting with the paper done by Lazarian and Vishniac [Astrophys. J. 517, 700–718 (1999)] proposed that 3D turbulence makes magnetic reconnection fast and that magnetic reconnection and turbulence are intrinsically connected. In particular, we discuss the dramatic violation of the textbook concept of magnetic flux-freezing in the presence of turbulence. We demonstrate that in the presence of turbulence, the plasma effects are subdominant to turbulence as far as the magnetic reconnection is concerned. The latter fact justifies a magnetohydrodynamiclike treatment of magnetic reconnection on all scales much larger than the relevant plasma scales. We discuss the numerical and observational evidence supporting the turbulent reconnection model. In particular, we demonstrate that the tearing reconnection is suppressed in 3D, and unlike the 2D settings, 3D reconnection induces turbulence that makes magnetic reconnection independent of resistivity. We show that turbulent reconnection dramatically affects key astrophysical processes, e.g., star formation, turbulent dynamo, and acceleration of cosmic rays. We provide criticism of the concept of “reconnection-mediated turbulence” and explain why turbulent reconnection is very different from enhanced turbulent resistivity and hyper-resistivity and why the latter have fatal conceptual flaws.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Line-of-sight observations at 86 GHz with a very large and a small antenna

Amplitude variations over a 12.9 km terrestrial line-of-sight path were measured simultaneously on a 1400 lambda and a 29 lambda antenna at 86.16 GHz. Clear atmosphere data from two occasions with considerably different meteorological conditions are presented. Both sets have statistical and spectral parameters in good agreement with turbulence theory. Some of the data taken after a thunderstorm front passage show a slow gain reduction of the large antenna of up to 2 dB and an increase in variance to a level above that of the small antenna. The power spectral density of these data reveals that the excess fluctuation power is in the region of the spectrum which turbulence theory predicts to be flat. It shows an approximate 1/f dependence. It is attributed to refractive bending of up to 0.025 deg. Gain reductions due to turbulence or turbulence induced angle-of-arrival variations were estimated to be negligible.

Vogel, W. J.↗
NASA NTRS1956

Charts Adapted from Van Driest's Turbulent Flat-plate Theory for Determining Values of Turbulent Aerodynamic Friction and Heat-transfer Coefficients

A modified method of Van Driest's flat-plate theory for turbulent boundary layer has been found to simplify the calculation of local skin-friction coefficients which, in turn, have made it possible to obtain through Reynolds analogy theoretical turbulent heat-transfer coefficients in the form of Stanton number. A general formula is given and charts are presented from which the modified method can be solved for Mach numbers 1.0 to 12.0, temperature ratios 0.2 to 6.0, and Reynolds numbers 0.2 times 10 to the 6th power to 200 times 10 to the 6th power.

HEAT TRANSFER, AERODYNAMIC↗
NASA NTRS1997

Time Correlations and the Frequency Spectrum of Sound Radiated by Turbulent Flows

Theories of turbulent time correlations are applied to compute frequency spectra of sound radiated by isotropic turbulence and by turbulent shear flows. The hypothesis that Eulerian time correlations are dominated by the sweeping action of the most energetic scales implies that the frequency spectrum of the sound radiated by isotropic turbulence scales as omega(exp 4) for low frequencies and as omega(exp -3/4) for high frequencies. The sweeping hypothesis is applied to an approximate theory of jet noise. The high frequency noise again scales as omega(exp -3/4), but the low frequency spectrum scales as omega(exp 2). In comparison, a classical theory of jet noise based on dimensional analysis gives omega(exp -2) and omega(exp 2) scaling for these frequency ranges. It is shown that the omega(exp -2) scaling is obtained by simplifying the description of turbulent time correlations. An approximate theory of the effect of shear on turbulent time correlations is developed and applied to the frequency spectrum of sound radiated by shear turbulence. The predicted steepening of the shear dominated spectrum appears to be consistent with jet noise measurements.

Rubinstein, Robert↗
NASA NTRS1972

The large Reynolds number - Asymptotic theory of turbulent boundary layers.

A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.

Mellor, G. L.↗
NASA NTRS1974

Acoustical theory of turbulence

Fluid functions are expanded in a series of functions constituting a complete and orthogonal system of wave solutions of the linearized Navier-Stokes system. The motion of characteristic waves is described by Hamiltonian equations of ray acoustics. Amplitude of the waves is described with the aid of nonlinear interaction terms. The distribution functions (squares of amplitudes) satisfy Boltzmann-type equations and completely describe the mean turbulence properties.

Kentzer, C. P.↗
NASA NTRS1984

Advances in Multivalued-Velocity Theory of Turbulence

Developments reported in modeling of fluid turbulence as superposition of number of interpenetrating velocity fields. Multivalued-velocity model has practical implications in design of aircraft, turbines, nozzles, pumps, and other systems that involve turbulent flow. In both viscous and inviscid cases, equations made to predict stable regine of oscillations, both finite and independent of initial conditions as in case of real turbulence.

Zak, M. A.↗
NASA NTRS1985

On the relation between 'mixing length' and 'direct interaction approximation' theories of turbulence

The capabilities of direct interaction approximations (DIA) and weak-coupling approximations (WCA) in modeling turbulence in plasma physics studies are examined. DIA and WCA formalisms are reviewed and a DIA expression for homogeneous incompressible hydrodynamics is simplified to derive an energy spectrum in an arbitrary wavenumber space. A solution is defined for the expression when applied to long wavelength phenomena generated by an instability. The equation is further generalized to yield a transport equation for modeling the spectrum generated by homogeneous turbulence in a linearly unstable system undergoing nonlinear interaction. Finally, the technique is applied to two-dimensional turbulence in a low pressure, weakly ionized plasma embedded in a homogeneous magnetic field and experiencing instabilities caused by electron density and electric potential gradients, such as found in the ionospheric E region.

Sudan, R. N.↗
NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗
NASA NTRS1986

A theory for turbulent curved wall jets

A simple theoretical model is proposed to describe the flow of a turbulent wall jet along a curved surface into a quiescent atmosphere. An integral method is used to solve the momentum equation and identifies three contributions to the spreading rate of the wall jet: (1) turbulent diffusion in the wall jet; (2) wall curvature; and (3) rate of change of wall curvature. Closed from approximate solutions are found for the case of a plane wall, a circular cylinder, and a logarithmic spiral surface. Comparison with experimental data for these three cases is made showing good agreement.

Roberts, Leonard↗
NASA NTRS1987

A theory for turbulent curved wall jets

An attempt is made to formulate the simplest possible model for the flow of a wall jet emanating from a two dimensional source into quiescent surroundings in the presence of a wall of arbitrary shape. The method used self similar profiles for the mean velocity together with a simple eddy viscosity model. The streamwise and radial momentum equations are integrated across the wall jet flow to give an expression for the momentum balance including the effect of the pressure gradient induced by the rate of change of surface curvature. The streamwise momentum equation is also evaluated at the point of maximum velocity to provide a second equation and thereby permit a solution for the two unknown quantities, the jet half width and the maximum velocity. This approach provides approximate closed form solutions for the flow of the wall jet over surfaces of various shapes, and in particular permits a direct comparison with the available experimental results for plane, cylindrical or logarithmic spiral surfaces.

Roberts, Leonard↗
NASA NTRS1958

On the statistical theory of turbulence

A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.

Heisenberg, W↗
NASA NTRS1980

Selective decay hypothesis at high mechanical and magnetic Reynolds numbers

Implications of certain applications of turbulence theory to two-dimensional turbulence and magnetohydrodynamic flow are discussed. It is shown that the use of the Navier-Stokes equation (NSE) for measurements of turbulent fluctuations has been effective only for three-dimensional flows. For two-dimensional flows, used for the study of large-scale motions in the atmosphere or ocean, enstrophy is cascaded to high wave numbers and dissipated at a finite rate even at infinite Re. MHD flows are numerically calculated for the two-dimensional case and analytically for the three-dimensional case, for which discrepancies in the relative rates of energy and cross helicity decay lead to a recommendation that numerical calculations for the three-dimensional case be carried out to determine the precise decayed states.

Matthaeus, W. H.↗
NASA NTRS1984

On the linear approximation of gravity wave saturation in the mesosphere

Lindzen's model of gravity wave breaking is shown to be inconsistent with the process of convective adjustment and associated turbulent outbreak. The K-theory turbulent diffusion model used by Lindzen implies a spatially uniform turbulent field which is not in agreement with the fact that gravity wave saturation and the associated convection produce turbulence only in restricted zones. The Lindzen model may be corrected to some extent by taking the turbulent Prandtl number for a diffusion acting on the wave itself to be very large. The eddy diffusion coefficients computed by Lindzen then become a factor of 2 larger and eddy transports of heat and constituents by wave fields vanish to first order.

Chao, W. C.↗
NASA NTRS1994

Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence

We study weak Alfvenic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of small-scale turbulence in the interstellar medium. We prove that resonant 3-wave interactions are absent. We also show that the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic turbulence -- which is widely accepted -- describes weak 3-wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4-wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfven wave and the pseudo Alfven wave. The three-dimensional inertial-range energy spectrum of 4-wave shear Alfven turbulence guessed from physical arguments reads E(k(sub z), k(sub perpendicular)) approximately V(sub A)v(sub L)L(exp -1/3)k(sub perpendicular)(exp -10/3), where V(sub A) is the Alfven speed, and v(sub L) is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across lambda(sub perpendicular) approximately k(sub perpendicular exp -1) is v(sub lambda (sub perpendicular)) is approximately v(sub L)(lambda(sub perpendicular)/L)(exp 2/3). We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in k-space, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4-wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, k(sub perpendicular)L is approximately (V(sub A)/v(sub L))(exp 3/2), weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4-wave inertial-range to be substantial. When the excitation is strong, the width of the 4-wave inertial-range shrinks to zero. This seems likely to be the case in the interstellar medium.

Sridhar, S.↗