Weak locally homogeneous turbulence and heat transfer with uniform normal strain
Weak locally homogeneous turbulence and heat transfer with uniform normal strain
COMPRESSIBLE FLOW↗
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Results for “weak turbulence”
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Mirroring in the Fokker-Planck coefficient for cosmic-ray pitch-angle scattering in homogeneous magnetic turbulence
The Fokker-Planck coefficient for pitch-angle scattering, appropriate for cosmic rays in homogeneous stationary magnetic turbulence is computed without making any specific assumptions concerning the statistical symmetries of the random field. The Fokker-Planck coefficient obtained can be used to compute the parallel diffusion coefficient for high-energy cosmic rays propagating in the presence of strong turbulence, or for low-energy cosmic rays in the presence of weak turbulence. Because of the generality of magnetic turbulence allowed for in the analysis, special interplanetary magnetic field features, such as discontinuities or particular wave modes, can be included rigorously.
Goldstein, M. L.↗
A Simple Theory of Capillary-Gravity Wave Turbulence
Employing a recently proposed 'multi-wave interaction' theory [JFM, 243, 623-625], spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The resultant absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear Rossby waves) intractable by small-perturbation techniques, even in the weak turbulence limit. The analytical solution obtained in the present work is shown to be in good agreement with experimental data. Its low- and high-frequency limits yield power-laws characterizing spectra of purely gravity and capillary waves, respectively. In the limits of weak and strong linearity, these reduce of the Zakharov-Filonenko and Phillips spectra, respectively.
Glazman, Roman E.↗
Effective viscosity, resistivity, and Reynolds number in weakly collisional plasma turbulence
ABSTRACT We examine dissipation and energy conversion in weakly collisional plasma turbulence, employing in situ observations from the Magnetospheric Multiscale mission and kinetic particle-in-cell simulations of proton–electron plasma. A previous result indicated the presence of viscous-like and resistive-like scaling of average energy conversion rates – analogous to scalings characteristic of collisional systems. This allows for extraction of collisional-like coefficients of effective viscosity and resistivity, and thus also determination of effective Reynolds numbers based on these coefficients. The effective Reynolds number, as a measure of the available bandwidth for turbulence to populate various scales, links turbulence macroscale properties with kinetic plasma properties in a novel way.
Astronomy & Astrophysics↗
Separated trailing-edge flow at a transonic Mach number
Results from an experimental investigation of a small-scale separated flow at a sharp trailing edge are presented. The separated flow was a result of sustained adverse pressure gradients. Experiments were carried out at a transonic Mach number, without any shock wave in the flow, and at a high Reynolds number. Measurements include surface pressure distributions, mean velocity, turbulent shear stress, turbulent kinetic energy, and some streamwise turbulence intensity profiles in the region from just upstream of separation to downstream into the near-wake, following wake-closure. The results show noticeable changes in the mean and turbulent quantities in the separated region although the wall adverse pressure gradients are relatively weak. Turbulent normal stress becomes important in the vicinity of separation and in the separated zone with regard to both mean-flow development and turbulence-energy production. The experimental data are used to assess the performance of two boundary-layer calculation methods.
Viswanath, P. R.↗
Shock-turbulence interactions in a reacting flow
A specific reactive flow configuration, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small amplitude shear waves) is addressed. The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one dimensional power spectra of these flow quantities is given.
Jackson, T. L.↗
A nonlinear theory of cosmic ray pitch angle diffusion in homogeneous magnetostatic turbulence
A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic ray pitch angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's resonance-broadening theory and contains no ad hoc approximations. A detailed calculation is presented for a model of slab turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.
Goldstein, M. L.↗
A Simple Theory of Capillary-Gravity Wave Turbulence
Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.
Glazman, Roman E.↗
Turbulent Concentration of Chondrules: Size Distribution and Multifractal Scaling
Size-selective concentration of particles in 3D turbulence may be related to collection of chondrules and other constituents into primitive bodies in a weakly turbulent protoplanetary nebula. In the terrestrial planet region, both the characteristic size and narrow size distribution of chondrules are explained, whereas "fluffier" particles would be concentrated in lower density, or more intensely turbulent, regions of the nebula. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a dose tie to the turbulent cascade process. This scaling behavior allows predictions of the concentration probabilities to be made in the protoplanetary nebula, which are so large (> 10(exp 3) - 10(exp 4)) that further studies must be made of the role of mass loading.
Cuzzi, Jeffrey N.↗
Role of collisionality and radiative cooling in supersonic plasma jet collisions of different materials
Currently there is considerable interest in creating scalable laboratory plasmas to study the mechanisms behind the formation and evolution of astrophysical phenomena such as Herbig-Haro objects and supernova remnants. Laboratory-scaled experiments can provide a well diagnosed and repeatable supplement to direct observations of these extraterrestrial objects if they meet similarity criteria demonstrating that the same physics govern both systems. Here, we present a study on the role of collision and cooling rates on shock formation using colliding jets from opposed conical wire arrays on a compact pulsed-power driver. These diverse conditions were achieved by changing the wire material feeding the jets, since the ion-ion mean free path (λmfp-ii) and radiative cooling rates (Prad) increase with atomic number. Low Z carbon flows produced smooth, temporally stable shocks. Weakly collisional, moderately cooled aluminum flows produced strong shocks that developed signs of thermal condensation instabilities and turbulence. Weakly collisional, strongly cooled copper flows collided to form thin shocks that developed inconsistently and fragmented. Effectively collisionless, strongly cooled tungsten flows interpenetrated, producing long axial density perturbations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Strong plasma turbulence in the earth's electron foreshock
A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.
Robinson, P. A.↗
Interaction of turbulence with a detonation wave
This paper addresses a specific reactive-flow configuration, namely, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small-amplitude vorticity waves). The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one-dimensional power spectra of these flow quantities are given.
Jackson, T. L.↗
A nonlinear theory of cosmic-ray pitch-angle diffusion in homogeneous magnetostatic turbulence
A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic-ray pitch-angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's 'resonance broadening' theory and contains no ad hoc approximations. A detailed calculation is presented for a model of 'slab' turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch-angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.
Goldstein, M. L.↗
Mesospheric gravity-wave climatology at Adelaide
The MF Adelaide partial-reflection radar has been operating continuously since November 1983. This has enabled a climatology of gravity-wave activity to be constructed for the mesosphere. The data have been analyzed for a medium-period range of 1 to 8 hr. and a longer period range between 8 and 24 hr. covering the inertio-period waves. The tidal motions have been filtered out prior to analysis. For the data analyses so far (Nov. 1983 to Dec. 1984), a number of interesting features emerged. Firstly, the wave activity at heights above 80 km shows a small seimannual variation with season with the activity being strongest in summer and winter. At heights below 80 km however, there is a similar but more marked variation with the weakest amplitudes occurring at the time of the changeovers in the prevailing circulation. If breaking gravity waves are responsible for much of the turbulence in the mesosphere, then the periods March to April and September to October might also be expected to be periods of weak turbulence. The wave field appears to be partially polarized. The meridional amplitudes are larger than the zonal amplitudes, especially in water. It is found that the degree of polarization is about 15% in summer and 30% in winter. The polarized component is found to propagate in the opposite direction to the background flow in the stratosphere, which suggests that the polarization arises through directional filtering of the waves as they propagate up from below.
Vincent, R. A.↗
Blowing in the Wind: II. Creation and Redistribution of Refractory Inclusions in a Turbulent Protoplanetary Nebula
Ca-Al rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overwhelm inward drift, and prevent significant numbers of CAI-size particles from being lost into the sun for times on the order of 10(exp 6) years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (less than or approx. equal to 0.1 mm diameter) CAIs persist for longer times than large (greater than or approx. equal to 5mm diameter ones). To obtain a quantitative match t o the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausably solar, as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO2 might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in l60 as inferred from CAIs and other high temperature condensates.
Cuzzi, Jeffrey N.↗
Blowing in the Wind: II. Creation and Redistribution of Refractory Inclusions in a Turbulent Protoplanetary Nebula
Ca-A1 rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overwhelm inward drift, and prevent significant numbers of CAI-size particles from being lost into the sun for times on the order of 10(exp 6) years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (less than or approximately 0.1 mm diameter) CAIs persist for longer times than large (greater than or approximately 5mm diameter ones. To obtain a quantitative match to the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausibly solar; as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO2 might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in O-16 as inferred from CAIs and other high temperature condensates.
Cuzzi, Jeffrey N.↗
Creation and Distribution of CAIs in the Protoplanetary Nebula
CaAl rich refractory mineral inclusions (CAIs) found at 1 - 10% mass fraction in primitive chondrites appear to be several million years older than the dominant (chondrule) components in the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We assess a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can prevent significant numbers of CAI-size particles from being lost into the sun for times of 1 - 3 x 10(exp 6) years. To match the CAI abundances quantitatively, we advocate an enhancement of the inner hot nebula in silicate-forming material, due to rapid inward migration of very primitive, silicate and carbon rich, meter-sized objects. 'Combustion' of the carbon into CO would make the CAI formation environment more reduced than solar, as certain observations imply. Abundant CO might also play a role in mass-independent chemical fractionation of oxygen isotopes as seen in CAIs and associated primitive, high-temperature condensates.
Cuzzi, J. N.↗
Turbulence-level dependence of cosmic ray parallel diffusion
ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.
79 ASTRONOMY AND ASTROPHYSICS↗