the relative velocity must be sought in the effect of the local mean magnetic field on the relative dispersion process. Al- though macroscopically the MHD system has no mean mag- netic field, on small spatial scales the slowly evolving large scale magnetic field fluctuations act like a mean magnetic field. It is a well known fact that in magnetohydrodynamic turbulence turbulent eddies are anisotropic with respect to a mean magnetic field. 43–48 As the fluid elements travel on av- erage preferentially along the magnetic lines of force the relative dispersion is significantly reduced in the field- perpendicular direction. Motions across field lines trigger quasi-oscillatory flow patterns which are supposed to drive the energy cascade 44 but apparently do not lead to an effec- tive separation of the particle pairs. This anisotropy causes the alignment of the particle separation vector ⌬ to the local mean magnetic field proxy B ¯ as observed in Fig. 7.
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A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Els¨asser field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multiexponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interpreted as evidence for the weakness, or absence, of a parallel magnetofluid turbulence energy cascade. As such, these results present strong observational constraints on the statistical nature of intermittency in turbulent plasmas.
We analyzed energy transfer processes induced by triad mode interactions in homogeneous, isotropic tur- bulence in magnetohydrodynamic (MHD) and Hall magnetohydrodynamic (HMHD) media. In particular, we analyzed the Fourier spectra of the energy transfers using geometric-series shell-partitioning methods, analogous to dyadic wavelet analysis. Snapshot datasets were collected once the MHD and HMHD turbulences had suﬃ- ciently developed. Graphs of all energy spectra were well collapsed after the normalization using the dissipation rates and the diﬀusion coeﬃcients, i.e. they showed good self-similarity. Despite such self-similarity of energy spectra, the transfer due to mode interactions between the ﬂuid advection and Hall term was reduced over time, while those due to the Lorentz force and induction remained rather stationary in regions of higher wave number.
A possible scenario is that sideband wave formation plays an important role in MHD turbulence and is moti- vated by the recent observational confirmation about the existence of sideband waves adjacent to the linear- mode branch in solar wind turbulence (Perschke et al. 2013, 2014) Energy transport in the frequency domain represents generation of sideband waves. For quasi-per- pendicular propagations, the fast mode has finite fre- quencies, while the other two MHD wave modes, Alfvèn and slow, have zero frequency. Sideband waves develop in such a way that the energy stored along the linear-mode branches flows toward sideband waves. The wave study shown in this manuscript indicates that it is unlikely to excite sideband waves toward higher frequencies. The energy transport in the frequency domain is slower than the transport in the wavenumber domain. Therefore, most of the fluctuation energies is constrained to lower frequencies, e.g., up to the frequencies of the fast mode. The sideband formation influences the wavevector ani- sotropy, as well. The observational result that most of the fluctuation energies are associated with quasi-perpendic- ular wavevectors to the mean magnetic field indicates a scenario that the sideband wave formation is not an iso- tropic process but anisotropic, presumably because the zero-frequency or nearly zero-frequency mode as real- ized by the perpendicular wavevector limit of the Alfvén and the slow modes are more essential in MHD turbu- lence. The wave evolution scenario into turbulence is illustrated in Fig. 10.
For hydrodynamics, isotropy and mirror symmetry remain reasonable approximations in many situations; however, an- isotropy is expected to become significant in a variety of circumstances. Preferred directions, such as might be associ- ated with rotation, or a large-scale gradient can have impact on locally homogeneous turbulence, and representation of the correlation tensors must allow for this possibility @ 7,16 # . Homogeneous turbulence can also depend on higher-order tensor quantities, such as the gradient tensor of a nonuniform mean flow, ~ see, e.g., @ 17 #! , although we do not consider such extensions here. In many cases symmetries with respect to tensor quantities and preferred directions have direct im- pact on the structure of the correlation tensors. This is espe- cially true for MHD turbulence for which, in many physical applications, there may be an influential local mean magnetic field direction that can induce spectral and spatial correlation anisotropy. ~ For a review of the extensively studied example of anisotropic turbulence in solar wind fluctuations, see @ 18 # . ! While axisymmetric representations may be adequate in some cases, there are clear motivations to go a step further and investigate the most general two-point, two-field corre- lations for incompressible homogeneous turbulence. For ex- ample, it is not uncommon to be presented simultaneously with two preferred directions, such as in the solar wind, with a mean magnetic field direction and a direction ~ heliocentric radial ! associated with mean large-scale gradients. Just as important, it turns out that the most general case is structur- ally no more complicated than the axisymmetric case @ 6–8 # . In this paper we present the full structure, using Cartesian coordinates, of the autocorrelation and cross-correlation ten- sors associated with the solenoidal velocity and magnetic fluctuations in homogeneous turbulence. This provides com- plete information concerning the structure of all second-
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It is worth mentioning that numerical simulations of two-dimensional turbulence have routinely used a variety of forcing that provides steady energy and enstrophy in- jection rates ǫ and η. This class of forcing includes white-noise and flow-dependent forcing. While such a class of forcing is numerically desirable and realistic in some sense, it may render equation (2.28) incompatible with the mathematical formulation leading to the desired estimate (2.42). Nevertheless, for the present approach, there are no technical difficulties in arriving at this estimate as an upper bound for the number of degrees of freedom in the present sense. An undesirable numerical artifact that does cause concern, however, is the build-up of energy at the largest scales, which is unavoid- able as a fundamental result of the dual cascade. Simulations use various large-scale dissipation mechanisms to absorb this large scale energy, with negative powers of the Laplacian (also called hypoviscosity by a number of authors) and mechanical friction (also known as Ekman drag in the geophysical context) in common use. The former primarily operates at large scales, and its effects on small scales are not well understood. The latter is scale neutral, removing enstrophy (and energy) at all scales. This has seri- ous ‘side effects’ on the small-scale dynamics. Most importantly, the vorticity remains bounded in the inviscid limit. Such behaviour is in sharp contrast to the Kraichnan picture, in which the enstrophy grows without bound as the enstrophy inertial range becomes increasingly wider for smaller viscosity. An undesirable consequence is that viscous dissipation of enstrophy vanishes in the inviscid limit (Constantin & Ramos, 2007). It follows that for steady or quasisteady dynamics at sufficiently small viscosity, frictional dissipation of enstrophy outweighs its viscous counterpart. The classical en- strophy inertial range then becomes a (frictional) dissipation range, possibly without dramatic changes in its appearance.
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The dynamics of the formation of current sheets and other small scale coherent structures is of great importance in understanding the intermittent cascade and its fate. Furthermore, current sheet formation may be quite dif- ferent in a large turbulent system than it is in a laboratory device in which the magnetic field to leading order is large scale, laminar, and controlled by exter- nal coils. For example, it is well known that ideal-MHD flows that develop in turbulence give rise to intense thin current-sheet structures (Frisch et al 1983; Wan et al 2013). The ideal process of current sheet generation, observed at short times in high resolution MHD simulations (Wan et al 2013), apparently gives essentially identical higher order magnetic increment statistics as are seen in comparable high Reynolds number simulations – so we can understand that intermittency and the drivers of the conditions that lead to reconnection are ideal processes. In retrospect, this could have been anticipated in Parker’s original discussion of coronal flux tube interactions (Parker 1972). Reconnec- tion may subsequently be triggered at these sites, resulting in dissipation of turbulent magnetic field.
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A detailed analysis of forward and inverse energy transfer processes due to the Hall term eﬀect in freely de- caying, homogeneous, isotropic Hall magnetohydrodynamics (HMHD) turbulence is performed through Fourier and wavelet analyses. We analyzed three snapshot datasets that were taken from such a period to allow the tur- bulence to develop suﬃciently with a nearly constant magnetic Reynolds number. Because the Fourier energy spectra in these snapshots show remarkable agreement after the normalization in terms of the dissipation rates and the diﬀusion coeﬃcients, they are considered as a universal equilibrium state. By analyzing the numerical solutions that are generated without any external forcing, it is confirmed that the inverse energy transfer due to the Hall term eﬀect is intrinsic to HMHD dynamics. Orthonormal divergence-free wavelet analysis reveals that nonlinear mode interactions contributing to the inverse energy transfer exhibit a nonlocal feature, while those for the forward transfer are dominated by a local feature.
We are not dealing with power spectra either but pri- marily with fluctuations from which secondarily power spectra can be calculated. Since it is clear from our analy- sis that velocity fluctuation spectra can be Taylor–Gali- lei transformed into frequency space (under the weak assumption of small turbulent fluctuation amplitudes compared with the solar wind flow speed, not with the Alfvén velocity), it is also clear (because the transforma- tion holds and is just subject to the observational, experi- mental, instrumental, methodological uncertainties and errors) that from the Galilei transformation, one directly obtains the spectrum of wavenumber fluctuations of the turbulent velocity. One even, if the measurements are precise enough, obtain the phase of the fluctuations which when calculating the power spectral density after- wards is generally lost. Maintaining it would provide a measure of the correlation length, an interesting prob- lem in inself. A practical advice from our approach is to take the velocity turbulence to find out what the original wavenumber spectrum was/is, not the magnetic field. From that mentioned above, the velocity turbulence can be Taylor–Galilei transformed into the spacecraft fre- quency frame, while the magnetic field cannot except from the extreme case of complete separation from mechanical turbulence—a case when the magnetic field will never become turbulent.
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flows. 5,7,9–11 Albeit a mathematically neat model for the pro- cess of suppression of turbulence by a magnetic field, this formulation is at odds with the situation in many real flows, where there is a steady energy input into large scales. For example, in continuous steel casting or in crystal growth, a constant level of turbulence is maintained by, respectively, nozzle jets or wall rotation and convection. Further difficulty associated with the decay model is that the statistical prop- erties of the flow cannot be reliably quantified in numerical simulations. Since our goal in this paper is precisely such quantification 共especially of the anisotropy characteristics兲, we chose to work with the model of forced flow. An artificial forcing is applied at the large length scales to simulate the energy input in real systems and generate a statistically steady flow over a long period of time.
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Most interestingly, this spectrum is of an inverse Kol- mogorov type. Because of the relation between the Hall fluctuations in density and electric–magnetic fields, one of course expects that the presence of the Hall effect in the ion- inertial range affects the shape of the density power spec- trum. This is indeed the case. In the ion-inertial-scale range the Hall effect seems to practically compensate for the gen- eral spectral Kolmogorov slope of the density power spec- trum, causing it to flatten substantially. Scaling-wise speak- ing, this is quite a strong effect, the degree of whose signature in observed density power spectra does, however, depend on the various scaling constants in the spectral contributions. One may, however, speculate that the notoriously frequently observed e k −1 slope in the density power spectra in the so- lar wind around the presumable ion-inertial-scale range, for example in Šafránková et al. (2015), may result from the con- tribution of the Hall effect to the inertial-range spectrum of ion-inertial-scale turbulence.
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In this article we have analyzed buoyancy oscillations, which may be considered to be slow MHD waves propagating along the magnetic ﬁ eld lines. We are motivated by contributing to the theory of determining global oscillations present in the solar atmosphere. There is growing evidence that oscillations from the solar interior penetrated deeply into the solar atmosphere. Good examples of such penetration are the reports of 5-minute oscillations in the lower solar atmosphere by e.g., Didkovsky et al. ( 2011, 2013 ) , and Ireland et al. ( 2015 ) . Here, we address perturbations, taking into account the role of gravity. We focus on buoyancy-driven magnetohydrodynamic waves. The full coupled governing equations for MHD perturbations can be shown to have exact solutions when the temperature is constant ( Zhugzhda 1979, see also Cally 2001; Mather & Erdélyi 2016 ) . For more complicated ( and realistic ) density pro ﬁ les, to the best of our knowledge, the governing equations cannot be solved exactly. We ﬁ nd that we are able to solve the resulting governing equation under certain simplifying assumptions that are applicable to solar atmospheric conditions.
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The explicitly stochastic parameterization described above results in SBL transitions that are qualitatively in agreement with observations. An example realization is presented in Fig. 10. In this realization radiative cooling leads initially to a steady increase in stratification and flow stability. Once the vSBL is established (around simulation hour 2) turbulence pulses occur (none of which are individually sufficient to ini- tiate a vSBL to wSBL transition). These turbulence pulses result in heat fluxes slightly larger than observed but of the right order of magnitude (e.g. Doran, 2004). The occurrence of multiple smaller turbulence pulses between simulation hours 6 and 7.5 slowly erodes the stratification until it is suf- ficiently weakened that a vSBL to wSBL transition occurs. Consistent with observations, the simulated vSBL to wSBL transition lags behind the occurrence of the last turbulence burst (AM19c). After the wSBL is established (about simu- lation hour 7.5) the stratification begins to increase again and a subsequent turbulence collapse occurs approximately 1.5 h later. This event duration is very close to the peak in the pdf of the wSBL event duration (cf. Fig. 4), providing further ev- idence that these recovery periods in the wSBL are related to internal dynamics.
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Pulsations observed at Earth are typically associated with magnetohydrodynamic (MHD) waves [Dungey, 1955; Takahashi et al., 2006; Keiling, 2009]. MHD waves are considered ultralow frequency (ULF) waves if their frequencies lie between ∼1 mHz and 1 Hz corresponding to periods ranging between 1 s and ∼17 m. These periods are much smaller than Earth’s rotation rate, so plasma conditions in the terrestrial magneto- sphere can be treated as stationary on ULF MHD wave timescales [Glassmeier et al., 2004]. Terrestrial MHD waves have numerous sources and can lead to eigenoscillations of the entire magnetosphere [e.g., Kivelson and Southwood, 1985]. Much of the magnetosphere can be treated as cold to a ﬁrst approximation, and in this regime there are two types of MHD waves: (i) the fast (compressional) wave and (ii) the shear Alfvén (noncompressional) wave. When the expected wavelengths are comparable to the scale of the magneto- sphere, the compressional eigenmodes give rise to global wave structures. In nonuniform plasmas, the purely transverse Alfvén mode can only occur localized to particular magnetic shells. However, the two wave modes can resonantly couple to set up magnetic ﬁeld line resonances (FLRs) [Southwood, 1974; Chen and Hasegawa, 1974] on the shells where the Alfvén mode dispersion relation is satisﬁed.
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The nonuniform nature of the two-dimensional magnetohydrodynamic interactions which produce observed coronal structures has been modelled by Priest (1988, hereafter Paper 1) as extended standing disturbances. Working in a semi-infinite rectangular region, a uniform plasma flow with an embedded magnetic field was considered. The plasma flow was assumed to be much less than the Alfven speed, thus neglecting the effect of inertial forces. Four possible types of interaction arise, namely,a fast-mode compression, a fast-mode expansion, a slow-mode compression, and a slow-mode expansion. As plasma moves along a magnetic fieldline, a fast-mode occurs if magnetic and plasma pressures are in phase. Otherwise, we have a slow-mode. A com pression occurs when the plasma pressure increases, whereas an expansion occurs when it decreases. For example, a fast-mode expansion occurs when both plasma and magnetic pressures decrease.
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Abstract Analytical models of solar atmospheric magnetic structures have been crucial for our understanding of magnetohydrodynamic (MHD) wave behaviour and in the devel- opment of the field of solar magneto-seismology. Here, an analytical approach is used to derive the dispersion relation for MHD waves in a magnetic slab of homogeneous plasma enclosed on its two sides by non-magnetic, semi-infinite plasma with different densities and temperatures. This generalises the classic magnetic slab model, which is symmetric about the slab. The dispersion relation, unlike that governing a symmetric slab, cannot be decou- pled into the well-known sausage and kink modes, i.e. the modes have mixed properties. The eigenmodes of an asymmetric magnetic slab are better labelled as quasi-sausage and quasi-kink modes. Given that the solar atmosphere is highly inhomogeneous, this has impli- cations for MHD mode identification in a range of solar structures. A parametric analysis of how the mode properties (in particular the phase speed, eigenfrequencies, and amplitudes) vary in terms of the introduced asymmetry is conducted. In particular, avoided crossings oc- cur between quasi-sausage and quasi-kink surface modes, allowing modes to adopt different properties for different parameters in the external region.
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Over recent years, high spatial and temporal resolution obser- vations have allowed many authors to identify the existence of a wide variety of magnetohydrodynamic (MHD) waves throughout the solar corona (e.g. Aschwanden et al. 1999, 2002; Verwichte et al. 2010; Threlfall et al. 2013; Duckenfield et al. 2018). Of particular interest to the current study is the evidence of waves propagating along coronal structures (e.g. De Moortel et al. 2000; McEwan & De Moortel 2006; Okamoto et al. 2007; Thurgood et al. 2014; Morton et al. 2015). Whilst estimates of the energy associated with these waves are not well constrained (see, for example, Tomczyk et al. 2007; McIntosh et al. 2011), it is hypothesised that they may contribute to the heating of the coronal plasma and / or the acceleration of the fast solar wind. We refer interested readers to reviews by Erdélyi & Ballai (2007), Parnell & De Moortel (2012), Arregui (2015), and references therein.
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Gordon and Hollweg (1983) considered the damping of magnetohydrodynamic surface waves in the solar corona by collisional dissipation. They excluded coronal holes from their analysis and confined their attention to dense coronal regions where collisions are more frequent. They made the assumption that the magnetic pressure dominates the thermal pressure so that the wave dynamics could be approximately evaluated by assuming the plasma to be cold. This is not an unreasonable assumption for the corona which is dominated by magnetic fields and therefore is a low beta plasma. Their main conclusion was that surface waves could dissipate in a reasonable distance in the solar corona only if their periods were shorter than a few tens of seconds and the magnitude of the magnetic field was comparable to that of the quiet corona (< lOG). Thus the collisional damping of surface waves may serve to heat the quiet coronal regions, if the wave periods are short enough. However, the large magnetic field strengths which are presumed to exist in coronal active regions (say about lOOG) suggests that collisional dissipation of surface waves is too weak to heat these regions.
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The ow is induced due to constantly accelerated and oscillating plate. Expressions for the corresponding velocity eld and the adequate tangential stress are determined by means of the Fourier sine transform. In an other paper Khan et al. (2008) concentrated on the unsteady ows of a magnetohydrodynamic (MHD) second grade uid lling a porous medium. The ow modeling involves modi ed Darcy's law. Three problems are considered. They are (i) starting ow due to an oscillating edge, (ii) starting ow in a duct of rectangular cross-section oscillating parallel to its length, and (iii) starting ow due to an oscillating pressure gradient. Analytical expressions of velocity eld and corresponding tangential stresses are developed.
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Behcet’s disease (BD) is a chronic inflammatory disorder that can affect many systems in the body. Cardiac involvement increases the risk of cardiovascular mortality and occurs in 1% - 5% of pa- tients with BD. Ventricular arrythmias are believed to be the cause of this increased risk of car- diovascular mortality and it is also thought to be related with cardiac autonomic dysfunction. Heart rate turbulence (HRT) is a new predictor of cardiac autonomic activity. HRT is an inde- pendent and powerful predictor of mortality. In this study, we investigated the cardiac autonomic activity which can be determined by HRT in patients with BD. Forty patients with BD (20 men, mean age: 40 ± 9 years, range: 27 - 55 years) were diagnosed according to the International Study Group Criteria (ISGC) and gender and age matched healthy volunteers (20 men, mean age: 39 ± 8 years, range: 26 - 56 years) were included in this study. All of the participants (patients and con- trols) underwent 24 hours Holter electrocardiogram. HRT parameters, turbulence onset (TO) and turbulence slope (TS) were calculated with HRT (View Version 0.60-0.1 of Software Program). There were no significant differences in TO and TS values between patients with BD and control subject (TO-BD: 0.014 ± 0.03, TO-Control: 0.011 ± 0.04; TS-BD: 7.88 ± 4.9, TS-Control: 9.42 ± 6.7 respectively). Although increased cardiovascular mortality rates in BD have been shown in many studies, HRT values—detecting the risk of sudden death—do not seem to be altered in this disease.