Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

It is shown how suitably scaled, order-m moments, D-m(+/-), of the Elsasser vorticity fields in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P-M = 1. These vorticity fields are defined by omega(+/-) = curl z(+/-) = omega +/- j, where z(+/-) are Elsasser variables, and where omega and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q(+/-) that characterize the inertial range power-law dependencies of the z(+/-) energy spectra, epsilon(+/-)(k), are then examined, and bounds are obtained. Comments are also made on (a) the generalization of our results to the case P-M not equal 1 and (b) the relation between D-m(+/-) and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.

均匀各向同性湍流的频率波数能量谱

对均匀各向同性湍流的频率波数能量谱进行了初步研究，得出均匀各向同性湍流中能量随时间、空间尺度分布的解析表达式，并运用直接数值模拟的方法对理论预测进行验证．数值结果很好地支持了理论预测：横扫速度是决定频率波数能量谱的特征量．

Large eddy simulations for fan-OGV broadband noise prediction

The work in this paper forms part of a project on the use of large eddy simulation (LES) for broadband rotor-stator interaction noise prediction. Here we focus on LES of the flow field near a fan blade trailing edge. The first part of the paper aims to evaluate LES suitability for predicting the near-field velocity field for a blunt NACA-0012 airfoil at moderate Reynolds numbers (2× 10 5 and 4× 10 5). Preliminary computations of turbulent mean and root-mean-square velocities, as well as energy spectra at the trailing edge, are compared with those from a recent experiment.1 The second part of the paper describes preliminary progress on an LES calculation of the fan wakes on a fan rig. 2 The CFD code uses a mixed element unstructured mesh with a median dual control volume. A wall-adapting local eddy-viscosity sub-grid scale model is employed. A very small amount of numerical dissipation is added in the numerical scheme to keep the compressible solver stable. Further results for the fan turbulentmean and RMS velocity, and especially the aeroacoustics field will be presented at a later stage. Copyright © 2008 by Qinling LI, Nigel Peake & Mark Savill.

Grid-refined LES predictions for Fan-OGV broadband noise

This work forms part of a project on the use of large eddy simulation (LES) for broadband rotor-stator interaction noise prediction. In this paper, we focus on LES calculations of noise sources on and close to a blade trailing edge. We consider two test cases; one an isolated NACA0012 airfoil in flow, and the other an industry-standard rotating fan. In the first case, turbulent mean and RMS velocities and energy spectra at different locations are compared with those from experiment. 1,2The sound generated by the unsteady pressure fluctuations on the airfoil surface and by the flow turbulence will be predicted using a Ffowcs Williams Hawkings (FW-H) surface. In the second case, unsteady flow and acoustic fields around the blade passage 3 are presented for a refined mesh, and the rotor-stator tonal noise will be predicted by using the rotor-wake mean velocity profile and the methodology described in Lloyd & Peake 4. Copyright © 2009 by Qinling Li, Nigel Peake & Mark Savill.

On the computation of space-time correlations by large-eddy simulation

The effect of subgrid-scale (SGS) modeling on velocity (space-) time correlations is investigated in decaying isotropic turbulence. The performance of several SGS models is evaluated, which shows superiority of the dynamic Smagorinsky model used in conjunction with the multiscale large-eddy simulation (LES) procedure. Compared to the results of direct numerical simulation, LES is shown to underpredict the (un-normalized) correlation magnitude and slightly overpredict the decorrelation time scales. This can lead to inaccurate solutions in applications such as aeroacoustics. The underprediction of correlation functions is particularly severe for higher wavenumber modes which are swept by the most energetic modes. The classic sweeping hypothesis for stationary turbulence is generalized for decaying turbulence and used to analyze the observed discrepancies. Based on this analysis, the time correlations are determined by the wavenumber energy spectra and the sweeping velocity, which is the square root of the total energy. Hence, an accurate prediction of the instantaneous energy spectra is most critical to the accurate computation of time correlations. (C) 2004 American Institute of Physics.

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation (LES) to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale (SGS) model can correctly predict Lagrangian time correlations (LTCs). Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation (DNS) and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid-scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.

Influence of Coulomb potential for photoionization of H atoms in an elliptically polarized laser field: Velocity gauge versus length gauge

We theoretically study the influence of Coulomb potential for photoionization of hydrogen atoms in an intense laser field with elliptical polarization. The total ionization rates, photoelectron energy spectra, and photoelectron angular distributions are calculated with the Coulomb-Volkov wave functions in the velocity gauge and compared with those calculated in the length gauge as well as those calculated with the Volkov wave functions. By comparing the results obtained by the Coulomb-Volkov and Volkov wave functions, we find that for linear polarization the influence of Coulomb potential is obvious for low-energy photoelectrons, and as the photoelectron energy and/or the laser intensity increase, its influence becomes smaller. This trend, however, is not so clear for the case of elliptical polarization. We also find that the twofold symmetry in the photoelectron angular distributions for elliptical polarization is caused by the cooperation of Coulomb potential and interference of multiple transition channels. About the gauge issue, we show that the difference in the photoelectron angular distributions obtained by the velocity and length gauges becomes rather obvious for elliptical polarization, while the difference is generally smaller for linear polarization.

Ionization suppression of diatomic molecules in strong laser fields

The ionization rate of molecules in intense laser fields may be much lower than that of atoms with similar binding energy. This phenomenon is termed the ionization suppression of molecules and is caused by the molecular inner structure. In this paper, we perform a comprehensive study of the ionization suppression of homonuclear diatomic molecules in intense laser fields of linear and circular polarizations. We find that for linear polarization the total ionization rate and the ionization suppression depend greatly on the molecular alignment, and that for circular polarization the ionization suppression of molecules in the antibonding (bonding) shells disappears (appears) for laser intensities around 10(15) W/cm(2). We also find that the molecular photoelectron energy spectra are greatly changed by the interference effect, even though the total ionization rate of molecules remains almost the same as that of their companion atoms.

Effects on the proton production from explosions of hydrogen clusters subjected to intense femtosecond laser fields

The dependence of the maximum and average energies of protons, which were produced in the interaction of an intense laser pulse (similar to 1 x 10(16) W cm(-2), 65 fs) with hydrogen clusters in a gas jet backed up to 80 bar at liquid nitrogen temperature (similar to 80 K), on the backing pressure has been studied. The general trend of the proton energy dependence on the square of the average cluster radius, which is determined by a calibrated Rayleigh scattering measurement, is similar to that described by theory under the single size approximation. Calculations are made to fit the experimental results under a simplified model by taking into account both a log-normal cluster size distribution and the laser intensity attenuation in the interaction volume. A very good agreement between the experimental proton energy spectra and the calculations is obtained in the high- energy part of the proton energy distributions, but a discrepancy of the fits is revealed in the low-energy part at higher backing pressures which are associated with denser flows. A possible mechanism which would be responsible for this discrepancy is discussed. Finally, from the fits, a variation of the cluster size distributions was revealed to be dependent on the gas backing pressure as well as on the evolving time of the gas flow of clusters.

Towards understanding the mixing characteristics of turbulent buoyant flows

This work proposes a new simulation methodology in which variable density turbulent flows can be studied in the context of a mixing layer with or without the presence of gravity. Specifically, this methodology is developed to probe the nature of non-buoyantly-driven (i.e. isotropically-driven) or buoyantly-driven mixing deep inside a mixing layer. Numerical forcing methods are incorporated into both the velocity and scalar fields, which extends the length of time over which mixing physics can be studied. The simulation framework is designed to allow for independent variation of four non-dimensional parameters, including the Reynolds, Richardson, Atwood, and Schmidt numbers. Additionally, the governing equations are integrated in such a way to allow for the relative magnitude of buoyant energy production and non-buoyant energy production to be varied.

The computational requirements needed to implement the proposed configuration are presented. They are justified in terms of grid resolution, order of accuracy, and transport scheme. Canonical features of turbulent buoyant flows are reproduced as validation of the proposed methodology. These features include the recovery of isotropic Kolmogorov scales under buoyant and non-buoyant conditions, the recovery of anisotropic one-dimensional energy spectra under buoyant conditions, and the preservation of known statistical distributions in the scalar field, as found in other DNS studies.

This simulation methodology is used to perform a parametric study of turbulent buoyant flows to discern the effects of varying the Reynolds, Richardson, and Atwood numbers on the resulting state of mixing. The effects of the Reynolds and Atwood numbers are isolated by looking at two energy dissipation rate conditions under non-buoyant (variable density) and constant density conditions. The effects of Richardson number are isolated by varying the ratio of buoyant energy production to total energy production from zero (non-buoyant) to one (entirely buoyant) under constant Atwood number, Schmidt number, and energy dissipation rate conditions. It is found that the major differences between non-buoyant and buoyant turbulent flows are contained in the transfer spectrum and longitudinal structure functions, while all other metrics are largely similar (e.g. energy spectra, alignment characteristics of the strain-rate tensor). Also, despite the differences noted between fully buoyant and non-buoyant turbulent fields, the scalar field, in all cases, is unchanged by these. The mixing dynamics in the scalar field are found to be insensitive to the source of turbulent kinetic energy production (non-buoyant vs. buoyant).

Elemental composition of solar energetic particles

The Low Energy Telescopes on the Voyager spacecraft are used to measure the elemental composition (2 ≤ Z ≤ 28) and energy spectra (5 to 15 MeV /nucleon) of solar energetic particles (SEPs) in seven large flare events. Four flare events are selected which have SEP abundance ratios approximately independent of energy/nucleon. The abundances for these events are compared from flare to flare and are compared to solar abundances from other sources: spectroscopy of the photosphere and corona, and solar wind measurements.

The selected SEP composition results may be described by an average composition plus a systematic flare-to-flare deviation about the average. For each of the four events, the ratios of the SEP abundances to the four-flare average SEP abundances are approximately monotonic functions of nuclear charge Z in the range 6 ≤ Z ≤ 28. An exception to this Z-dependent trend occurs for He, whose abundance relative to Si is nearly the same in all four events.

The four-flare average SEP composition is significantly different from the solar composition determined by photospheric spectroscopy: The elements C, N and O are depleted in SEPs by a factor of about five relative to the elements Na, Mg, Al, Si, Ca, Cr, Fe and Ni. For some elemental abundance ratios (e.g. Mg/O), the difference between SEP and photospheric results is persistent from flare to flare and is apparently not due to a systematic difference in SEP energy/nucleon spectra between the elements, nor to propagation effects which would result in a time-dependent abundance ratio in individual flare events.

The four-flare average SEP composition is in agreement with solar wind abundance results and with a number of recent coronal abundance measurements. The evidence for a common depletion of oxygen in SEPs, the corona and the solar wind relative to the photosphere suggests that the SEPs originate in the corona and that both the SEPs and solar wind sample a coronal composition which is significantly and persistently different from that of the photosphere.

The streaming of 1.3-2.3 MeV cosmic-ray protons during periods between prompt solar particle events

The anisotropy of 1.3 - 2.3 MeV protons in interplanetary space has been measured using the Caltech Electron/Isotope Spectrometer aboard IMP-7 for 317 6-hour periods from 72/273 to 74/2. Periods dominated by prompt solar particle events are not included. The convective and diffusive anisotropies are determined from the observed anisotropy using concurrent solar wind speed measurements and observed energy spectra. The diffusive flow of particles is found to be typically toward the sun, indicating a positive radial gradient in the particle density. This anisotropy is inconsistent with previously proposed sources of low-energy proton increases seen at 1 AU which involve continual solar acceleration.

The typical properties of this new component of low-energy cosmic rays have been determine d for this period which is near solar minimum. The particles have a median intensity of 0.06 protons/ cm^(2)-sec-sr-MeV and a mean spectral index of -3.15.The amplitude of the diffusive anisotropy is approximately proportional to the solar wind speed. The rate at which particles are diffusing toward the sun is larger than the rate at which the solar wind is convecting the particles away from the sun. The 20 to 1 proton to alpha ratio typical of this new component has been reported by Mewaldt, et al. (1975b).

A propagation model with κ_(rr) assumed independent of radius and energy is used to show that the anisotropy could be due to increases similar to those found by McDonald, et al. (1975) at ~3 AU. The interplanetary Fermi-acceleration model proposed by Fisk (1976) to explain the increases seen near 3 AU is not consistent with the ~12 per cent diffusive anisotropy found.

The dependence of the diffusive anisotropy on various parameters is shown. A strong dependence of the direction of the diffusive anisotropy on the concurrently measured magnetic field direction is found, indicating a κ_⊥ less than κ_∥ to be typical for this large data set.

The abundances of ultraheavy elements in the cosmic radiation

Analysis of the data from the Heavy Nuclei Experiment on the HEAO-3 spacecraft has yielded the cosmic ray abundances of odd-even element pairs with atomic number, Z, in the range 33 ≤ Z ≤60, and the abundances of broad element groups in the range 62 ≤ Z ≤83, relative to iron. These data show that the cosmic ray source composition in this charge range is quite similar to that of the solar system provided an allowance is made for a source fractionation based on first ionization potential. The observations are inconsistent with a source composition which is dominated by either r-process or s-process material, whether or not an allowance is made for first ionization potential. Although the observations do not exclude a source containing the same mixture of r- and s-process material as in the solar system. the data are best fit by a source having an r- to s-process ratio of 1.22^(+0.25)_(0.21), relative to the solar system The abundances of secondary elements are consistent with the leaky box model of galactic propagation, implying a pathlength distribution similar to that which explains the abundances of nuclei with Z<29.

The energy spectra of the even elements in the range 38 ≤ Z ≤ 60 are found to have a deficiency of particles in the range ~1.5 to 3 GeV/amu, compared to iron. This deficiency may result from ionization energy loss in the interstellar medium, and is not predicted by propagation models which ignore such losses. ln addition, the energy spectra of secondary elements are found to be different to those of the primary elements. Such effects are consistent with observations of lighter nuclei, and are in qualitative agreement with galactic propagation models using a rigidity dependent escape length. The energy spectra of secondaries arising from the platinum group are found to be much steeper than those of lower Z. This effect may result from energy dependent fragmentation cross sections.