Spectrum Of Turbulent Fluctuations Research Articles

Extended Cyclotron Resonant Heating of the Turbulent Solar Wind

Circularly polarized, nearly parallel propagating waves are prevalent in the solar wind at ion-kinetic scales. At these scales, the spectrum of turbulent fluctuations in the solar wind steepens, often called the transition range, before flattening at sub-ion scales. Circularly polarized waves have been proposed as a mechanism to couple electromagnetic fluctuations to ion gyromotion, enabling ion-scale dissipation that results in observed ion-scale steepening. Here we study Parker Solar Probe observations of an extended stream of fast solar wind ranging from ∼15 to 55 R ⊙. We demonstrate that, throughout the stream, transition range steepening at ion scales is associated with the presence of significant left-handed ion-kinetic-scale waves, which are thought to be ion cyclotron waves. We implement quasilinear theory to compute the rate at which ions are heated via cyclotron resonance with the observed circularly polarized waves given the empirically measured proton velocity distribution functions. We apply the Von Kármán decay law to estimate the turbulent decay of the large-scale fluctuations, which is equal to the turbulent energy cascade rate. We find that the ion cyclotron heating rates are correlated with, and amount to a significant fraction of, the turbulent energy cascade rate, implying that cyclotron heating is an important dissipation mechanism in the solar wind.

Развитие турбулентности за околоземной ударной волной в периоды спокойного и возмущенного солнечного ветра

Magnetosheath is a transition layer between the solar wind and the magnetosphere and may contribute to the geoeffectiveness of various large-scale interplanetary phenomena. In this paper, we examine the dynamics of the turbulent fluctuation spectra behind the bow shock during undisturbed solar wind and when interplanetary coronal mass ejections and corotation interaction regions interact with the magnetosphere. The study is based on statistical analysis of the turbulence features inside the magnetosheath at different distances from the bow shock. We demonstrate that the turbulence features change when plasma crosses the bow shock for the solar wind of all types and they usually recover when plasma moves away from the bow shock. However, peculiarities in the turbulence development occur during interplanetary coronal mass ejections. Moreover, during disturbed solar wind there are relations between the turbulence features at the sub-ion scales and background plasma parameters such as plasma parameter β, the angle θBN between the interplanetary magnetic field and the local bow shock normal, solar wind bulk velocity, and the distance to the magnetosheath boundaries.

Turbulence development behind the bow shock during disturbed and undisturbed solar wind

Magnetosheath is a transition layer between the solar wind and the magnetosphere and may contribute to the geoeffectiveness of various large-scale interplanetary phenomena. In this paper, we examine the dynamics of the turbulent fluctuation spectra behind the bow shock during undisturbed solar wind and when interplanetary coronal mass ejections and corotation interaction regions interact with the magnetosphere. The study is based on statistical analysis of the turbulence features inside the magnetosheath at different distances from the bow shock. We demonstrate that the turbulence features change when plasma crosses the bow shock for the solar wind of all types and they usually recover when plasma moves away from the bow shock. However, peculiarities in the turbulence development occur during interplanetary coronal mass ejections. Moreover, during disturbed solar wind there are relations between the turbulence features at the sub-ion scales and background plasma parameters such as plasma parameter β, the angle θBN between the interplanetary magnetic field and the local bow shock normal, solar wind bulk velocity, and the distance to the magnetosheath boundaries.

The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer

The wave turbulence interactions in the stable boundary layer (SBL) of the atmosphere are studied based on data from lidar measurements of the vertical component of wind velocity during the propagation of internal gravity waves (IGWs). It is shown that as an IGW appears, the amplitude of the spectra of turbulent fluctuations of vertical wind velocity nearby the frequency of quasi-harmonic oscillations induced by an IGW increases significantly, sometimes by several orders of magnitude, compared to the spectra in the absence of an IGW. Since IGW energy is transferred to small-scale turbulence, the amplitude of spectra with the Kolmogorov–Obukhov −5/3 power-law frequency dependence in the inertial frequency range increases. The slope of the spectra in the low-frequency range between the frequency of IGW-induced oscillations and the frequency of the lower boundary of the inertial range exceeds the slope, corresponding to the −5/3 power-law dependence. In this frequency range, the spectra obey the power-law dependence on the frequency with the exponent ranging from −4.2 to −1.9. The average value of the exponent −3 is consistent with a low-frequency slope caused by IGWs in turbulent spectra in the lower SBL.

Applicability of Taylor’s hypothesis during Parker Solar Probe perihelia

We investigate the validity of Taylor’s hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvénic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameterϵ = δu0/√2V⊥, which quantifies the ratio between the typical speed of large-scale fluctuations,δu0, and the local perpendicular PSP speed in the solar wind frame,V⊥. TH is expected to be applicable forϵ≲ 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach numberMA=VSW∕VA, whereVSWandVAare the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameterϵis below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30°. For angles above 30°, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrumE(k⊥) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation’s energy across scales in the plasma frame.

Experimental investigation of turbulent fluctuation characteristics observed at a moving point under crossflows

In this study, the flow characteristics of turbulent fluctuations observed at a moving point under crossflows are experimentally investigated. For this, an experimental system is developed in which a measuring probe is able to move across a flow field with a moderate velocity, and the velocity of the probe can be adjusted freely within a certain range. The experimental results are compared to those of Balzer’s and Cooper’s models — two spectral models commonly used in current theoretical research and practical applications relative to moving vehicles. The results indicate that the flow characteristics experienced by a moving point are different from those experienced by a stationary point. For a fixed crossflow velocity, as the velocity of the moving point increases, the turbulence integral scale of longitudinal velocity fluctuations decreases, and the longitudinal turbulence spectrum shifts toward high frequencies correspondingly. A semi-elliptic model is proposed to qualitatively estimate the turbulence integral scale measured at a moving point. The flow characteristics experienced by a moving point exhibit an apparent Doppler effect. Furthermore, the deviation of Balzer’s model is pointed out, and the dominant causes for this effect are discussed, while the accuracy of Cooper’s model is verified through an experimental approach for the first time. Additionally, it is demonstrated that the von Kármán longitudinal spectrum can also be adapted to estimate the spectrum of turbulent fluctuations observed at a moving point. This work provides more data for the current research of flow characteristics relative to moving vehicles as well as other moving objects, which could be useful for analyzing the stability of a moving object under crossflows.

Astrophysical gyrokinetics: turbulence in pressure-anisotropic plasmas at ion scales and beyond

We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. The turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion-Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (J. Plasma Phys., vol. 81, 2015, 325810501). At scales at and below the ion-Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalization of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvénic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfvén waves transition into kinetic Alfvén waves. Secondly, we derive and discuss a very general gyrokinetic free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfvén waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy, even within the bounds imposed on it by firehose and mirror instabilities, can cause order-of-magnitude variations in the ion-to-electron heating ratio due to the dissipation of Alfvénic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects turbulent fluctuation spectra, the differential heating of particle species and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.

Three-dimensional extinction mapping using Gaussian random fields

We present a scheme for using stellar catalogues to map the three-dimensional distributions of extinction and dust within our Galaxy. Extinction is modelled as a Gaussian random field, whose covariance function is set by a simple physical model of the interstellar medium that assumes a Kolmogorov-like power spectrum of turbulent fluctuations. As extinction is modelled as a random field, the spatial resolution of the resulting maps is set naturally by the data available; there is no need to impose any spatial binning. We verify the validity of our scheme by testing it on simulated extinction fields and show that its precision is significantly improved over previous dust-mapping efforts. The approach we describe here can make use of any photometric, spectroscopic or astrometric data; it is not limited to any particular survey. Consequently, it can be applied to a wide range of data from both existing and future surveys.

Formation of strong stationary vortex turbulence in the terrestrial magnetosheath

The microscopic consequences of the presence of nonlinear vortex structures in the near-Earth plasma dispersive medium are studied in this work. In dispersive media, strongly localized vortex structures contain trapped particles, cause pronounced density fluctuations, and intensify transfer processes, mixing in a medium; i.e., they can form strong vortex turbulence. Turbulence is represented as a gas in the ensemble of strongly localized (therefore, weakly interacting) identical vortices composing the ground state. Vortices with different amplitudes are randomly located in space (since they interact with one another) and are described statistically. It is assumed that the steady turbulent state is formed through a balance of mutually competing effects: spontaneous generation of vortices due to nonlinear steepening of the disturbance front, ^noise transfer to small scales, and collisional or collisionless damping of disturbances in the HF region. Noise scaling in the inertial interval takes place since structures merge during their collision. A magnetized plasma medium in the magnetosheath is considered. A new type of turbulent fluctuation spectra with respect to wavenumbers k −8/3, which is in satisfactory agreement with satellite observations in space plasma, has been determined. The medium particle diffusion on an ensemble of vortices has also been studied. It has been established that the interaction between structures themselves and between structures and medium particles causes anomalous diffusion in the medium. The effective diffusion coefficient square roothly depends on the noise stationary level.

Model of strong stationary vortex turbulence in space plasmas

Abstract. This paper investigates the macroscopic consequences of nonlinear solitary vortex structures in magnetized space plasmas by developing theoretical model of plasma turbulence. Strongly localized vortex patterns contain trapped particles and, propagating in a medium, excite substantial density fluctuations and thus, intensify the energy, heat and mass transport processes, i.e., such vortices can form strong vortex turbulence. Turbulence is represented as an ensemble of strongly localized (and therefore weakly interacting) vortices. Vortices with various amplitudes are randomly distributed in space (due to collisions). For their description, a statistical approach is applied. It is supposed that a stationary turbulent state is formed by balancing competing effects: spontaneous development of vortices due to nonlinear twisting of the perturbations' fronts, cascading of perturbations into short scales (direct spectral cascade) and collisional or collisionless damping of the perturbations in the short-wave domain. In the inertial range, direct spectral cascade occurs through merging structures via collisions. It is shown that in the magneto-active plasmas, strong turbulence is generally anisotropic Turbulent modes mainly develop in the direction perpendicular to the local magnetic field. It is found that it is the compressibility of the local medium which primarily determines the character of the turbulent spectra: the strong vortex turbulence forms a power spectrum in wave number space. For example, a new spectrum of turbulent fluctuations in k−8/3 is derived which agrees with available experimental data. Within the framework of the developed model particle diffusion processes are also investigated. It is found that the interaction of structures with each other and particles causes anomalous diffusion in the medium. The effective coefficient of diffusion has a square root dependence on the stationary level of noise.

Stability and variations of plasma parameters in the L-2M stellarator during excitation of the induction current in the regime of ECR plasma heating

Results are presented from experimental studies of variations in the plasma parameters during the excitation of a multiaxis magnetic configuration by the induction current (up to 17 kA) in the basic magnetic configuration of the L-2M stellarator in the regime of ECR heating at a microwave power of ∼200 kW (∼1 MW m−3) and an average plasma density of (1–2) × 1019 m−3. The current direction was chosen to reduce the net rotational transform (the so-called “negative“ current). The current was high enough for the rotational transform to change its sign inside the plasma column. Computer simulations of the L-2M magnetic structure showed that the surface with a zero rotational transform is topologically unstable and gives rise to magnetic islands, i.e., to a multiaxis magnetic configuration. Magnetic measurements showed that, at negative currents above 10 kA, intense bursts of MHD oscillations with a clearly defined toroidal mode number n = 0 were observed in the frequency range of several kilohertz. Unfortunately, the experimental data are insufficient to draw the final conclusion on the transverse structure of these oscillations. The radial temperature profiles along the stellarator major radius in the equatorial plane were studied. It is found that the electron temperature decreases by a factor of 1.3 in the plasma core (r/a ≤ 0.6) and that the temperature jump is retained near the boundary. A change in turbulent fluctuations of the plasma density during the excitation of a negative current was studied using wave scattering diagnostics. It is found that the probability density function of the increments of fluctuations in the plasma core differs from a Gaussian distribution. The measured distribution is heavy-tailed and broadens in the presence of the current. It is found that the spectrum of turbulent fluctuations and their Doppler shift near the plasma boundary are nonuniform in the radial direction. This may be attributed to the shear of the poloidal velocity. The experimental results indicate that the formation of regions with a zero rotational transform in the plasma core somewhat intensifies plasma transport.

Stochasticity formation in a thick spherical layer for different methods of variation of the boundary conditions

The influence of the mode of formation of the flow in a rotating spherical layer on the parameters of steady-state chaotic regimes is studied experimentally near the limit of onset of these regimes. The case of counter-rotating boundaries of a thick spherical layer, whose thickness is equal to the inner-sphere radius, is considered. With the reference to two different flow formation conditions, namely, a sequential and a simultaneous increase in the angular velocity of the spherical boundaries, the possibility of transition to stochastic flow regimes with different turbulent-fluctuation spectra and different values of the correlation dimension is demonstrated.

Experimental study of the electromagnetic component of drift-wave turbulence

The magnetic turbulent fluctuation spectrum is investigated in the core of a toroidally confined plasma with parameters similar to those in the fusion edge plasma. The measured spectra show fully developed turbulence over almost 6 decades down to the range of nano-Tesla field amplitudes. The magnetic fluctuations are interpreted as being due to the parallel dynamics of drift-wave turbulence. The predicted strong β dependence of the magnetic fluctuations is experimentally confirmed. For the present parameters, anomalous transport due to the magnetic turbulence can be neglected compared with the electrostatic contribution.

Verification of gyrokinetic δf simulations of electron temperature gradient turbulence

The GEM gyrokinetic δf simulation code [Y. Chen and S. Parker, J. Comput. Phys. 189, 463 (2003); Y. Chen and S. Parker, J. Comput. Phys.220, 839 (2007)] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [W. M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G. W. Hammett, F. Jenko, M. J. Pueschel, and D. E. Shumaker, Phys. Plasmas 13, 122306 (2006)]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.

Zonal flow in toroidal ion temperature gradient mode turbulence

AbstractThe properties of zonal flows in the toroidal ion temperature gradient mode turbulence are investigated taking into account the polarization drift effects. The stability criterion and the characteristic oscillation frequency of the zonal flow are determined in terms of the spectra of turbulent fluctuations. The nonlinear evolution of zonal flows may lead to the formation of stationary long-lived coherent structures supporting stationary shear layers. These results indicate the existence of regions with reduced levels of anomalous transport attributed to zonal flows generalizing previous findings regarding zonal flows in electron drift turbulence.

Foreword to the Special Issue on Computational Heat Transfer

Foreword to the Special Issue on Computational Heat Transfer

Dissipation length scales in turbulent nonpremixed jet flames

Line imaging of Raman/Rayleigh/CO-LIF is used to investigate the energy and dissipation spectra of turbulent fluctuations in temperature and mixture fraction in several flames, including CH 4/H 2/N 2 jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and DLR-B) and piloted CH 4/air jet flames at Reynolds numbers of 13,400, 22,400, and 33,600 (Sandia flames C, D, and E). The high signal-to-noise ratio of the 1D Rayleigh scattering images enables determination of the turbulent cutoff wavenumber from 1D dissipation spectra. The local length scale inferred from this cutoff is analogous to the Batchelor scale in nonreacting flows. The measured thermal dissipation spectra in the turbulent flames are shown to be similar to the model spectrum of Pope for turbulent kinetic energy dissipation. Furthermore, for flames with Lewis number near unity, the 1D dissipation spectra for temperature and mixture fraction are shown to follow nearly the same rolloff in the high-wavenumber range, such that the cutoff length scale for thermal dissipation is equal to or slightly smaller than the cutoff length scale for mixture fraction dissipation. Measurements from the piloted CH 4/air flames are used to demonstrate that a surrogate cutoff scale may be obtained from the dissipation spectrum of the inverse of the Rayleigh signal itself, even when the Rayleigh scattering cross section varies through the flame. This suggests that the cutoff length scale determined from Rayleigh scattering measurements may be used to define the local resolution requirements and optimal data processing procedures for accurate determination of the mean mixture fraction dissipation, based upon Raman scattering measurements or other multiscalar imaging techniques.

Chemical composition of dust clouds in turbulent brown dwarf atmospheres

AbstractBrown dwarf atmospheres are largely convective. These convective gas flows collide and feed back a whole spectrum of turbulent fluctuations into the atmospheric fluid field. Resulting non-static density and temperature fields influence the local chemistry concerning gas phase and dust formation. Numerical simulations are used to show the large and inhomogeneous changes of the gas phase chemistry in a turbulent dust forming cloud region of a brown dwarf atmosphere. The relaxation time scale of the gas phase composition towards steady state is considerably longer than for the dust component.

Large-scale flows and coherent structure phenomena in flute turbulence

The properties of zonal and streamer flows in the flute mode turbulence are investigated. The stability criteria and the frequency of these flows are determined in terms of the spectra of turbulent fluctuations. Furthermore, it is shown that zonal flows can undergo a further nonlinear evolution leading to the formation of long-lived coherent structures which consist of self-bound wave packets supporting stationary shear layers, and thus can be characterized as regions with a reduced level of anomalous transport.

Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics

The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is shown, where the system reaches a state that is characterized by the ratio between the Alfvén time (the time for incompressible MHD waves to travel along the field lines) and the convective time scale of the driving motions. This ratio of time scales determines the energy spectra and the relaxation toward different regimes ranging from weak to strong turbulence. A connection is made with phenomenological theories for the energy spectra in MHD turbulence.