Nonlinear phenomena and turbulence are central to our understanding and modeling the dynamics of fluids and plasmas, and yet they still resist analytical resolutions in many instances. However, progress has been made recently, displaying a richness of phenomena which was somewhat unexpected a few years back, such as the double constant-flux cascades of a same invariant to both the large and to the small scales, or the presence of non-Gaussian wings in the large-scale fields, for fluids and plasmas. Here, I will concentrate on the direct measurement of the magnitude of dissipation and an evaluation of intermittency in a turbulent plasma using exact laws stemming from invariance principles and involving cross-correlation tensors with both the velocity and the magnetic fields. I will illustrate these points through scaling laws, together with data analysis from existing experiments, observations and numerical simulations. Finally, I will also briefly explore the possible implications for validity and use of several modeling strategies. To appear, Plasma Physics and Controlled Fusion, 2023.
We present a simple model for the turbulent kinetic energy behavior of subsonic plasma turbulence undergoing isotropic three-dimensional compression, such as may exist in various inertial confinement fusion experiments or astrophysical settings. The plasma viscosity depends on both the temperature and the ionization state, for which many possible scalings with compression are possible. For example, in an adiabatic compression the temperature scales as $1/L^2$, with $L$ the linear compression ratio, but if thermal energy loss mechanisms are accounted for, the temperature scaling may be weaker. …
Compression of turbulent plasma can amplify the turbulent kinetic energy, if the compression is fast compared to the viscous dissipation time of the turbulent eddies. A sudden viscous dissipation mechanism is demonstrated, whereby this amplified turbulent kinetic energy is rapidly converted into thermal energy, suggesting a new paradigm for fast ignition inertial fusion.
The goal of this document is to present a detailed description of the goals, simulation setup and diagnostics for the Turbulent Dissipation Challenge (arXiv:1303.0204) as discussed in the Solar Heliospheric and INterplanetary Environment (SHINE) 2013 workshop, American Geophysical Union Fall Meeting 2013 and the accompanying antenna meeting in Berkeley.
Turbulent plasma flow, amplified by rapid 3D compression, can be suddenly dissipated under continuing compression. This effect relies on the sensitivity of the plasma viscosity to the temperature, $μ\sim T^{5/2}$. The plasma viscosity is also sensitive to the plasma ionization state. We show that the sudden dissipation phenomenon may be prevented when the plasma ionization state increases during compression, and demonstrate the regime of net viscosity dependence on compression where sudden dissipation is guaranteed. Additionally, it is shown that, compared to cases with no ionization, ionizati…
Evolution of the parametric decay instability (PDI) of a circularly polarized Aflvén wave in a turbulent low-beta plasma background is investigated using 3D hybrid simulations. It is shown that the turbulence reduces the growth rate of PDI as compared to the linear theory predictions, but PDI can still exist. Interestingly, the damping rate of ion acoustic mode (as the product of PDI) is also reduced as compared to the linear Vlasov predictions. Nonetheless, significant heating of ions in the direction parallel to the background magnetic field is observed due to resonant Landau damping of the …
The magnetic Reynolds number R_M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R_M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number, R_{M,e}, as the ratio of the advection to microphysical dissipation terms in the total magnetic energy e…
Heliospheric plasma turbulence plays a key role in transferring the energy of large-scale magnetic field and plasma flow fluctuations to smaller scales where the energy can be dissipated, ultimately leading to plasma heating. High-quality measurements of electromagnetic fields and electron velocity distributions by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath present a unique opportunity to characterize plasma turbulence and to determine the mechanisms responsible for its dissipation. We apply the field-particle correlation technique to a set of twenty MMS magnetosheath…
The goal of the present document is to present the idea of, and convince the community to participate in, Turbulent Dissipation Challenge. The idea was discussed in Solar Heliospheric and Interplanetary ENvironment (SHINE) 2012 meeting. The proponents of the idea Tulasi Parashar and Chadi Salem have prepared this document to circulate the idea in the community. The Turbulent Dissipation Challenge idea is to bring the community together and simulate the same set of problems and try to come to a common set of conclusions about the relative strengths of two different kinds of dissipative processe…
The kinetic evolution of the Orszag-Tang vortex is studied using collisionless hybrid simulations. In the magnetohydrodynamic regime this vortex leads rapidly to broadband turbulence. Significant differences from MHD arise at small scales, where the fluid scale energy dissipates into heat almost exclusively through the magnetic field because the protons are decoupled from the magnetic field. Although cyclotron resonance is absent, the protons heat preferentially in the plane perpendicular to the mean field, as in the corona and solar wind. Effective transport coefficients are calculated.
We present two-dimensional fully-kinetic Particle-in-Cell simulations of decaying electromagnetic fluctuations. The computational box is such that wavelengths ranging from electron to ion gyroradii are resolved. The parameters used are realistic for the solar wind, and the ion to electron mass ratio is physical. The understanding of the dissipation of turbulent fluctuations at small scales is thought to be a crucial mechanism for solar wind acceleration and coronal heating. The computational results suggest that a power law cascade of magnetic fluctuations could be sustained up to scales of th…
We present the first statistical study of magnetic structures and associated energy dissipation observed during a single period of turbulent magnetic reconnection, by using the \textit{in-situ} measurements of the Magnetospheric Multiscale mission in the Earth's magnetotail on July 26, 2017. The structures are selected by identifying a bipolar signature in the magnetic field and categorized as plasmoids or current sheets via an automated algorithm which examines current density and plasma flow. The size of the plasmoids forms a decaying exponential distribution ranging from sub-electron up to …
Relaminarization of wall-bounded turbulent flows by means of external static magnetic fields is a long-known phenomenon in the physics of electrically conducting fluids at low magnetic Reynolds numbers. Despite the large literature on the subject, it is not yet completely clear what combination of the Hartmann ($M$) and the Reynolds number has to be used to predict the laminar-turbulent transition in channel or pipe flows fed by upstream turbulent flows free of magnetic perturbations. Relying upon standard phenomenological approaches related to mixing length and structural concepts, we put for…
The non-modal approach for a linearized system differs from a normal mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the stability of a bi-Maxwellian magnetized plasma using the Landau fluid model, which we briefly describe. We show that bi-Maxwellian stable equilibria can support transient growth of some physical quantities, and we study how these transients behave when an equilibrium approaches its marginally stable condition. This is relevant to anisotropic plasma, that are …
It has been recognized that the turbulent cross helicity (correlation between the velocity and magnetic-field fluctuations) can play an important role in several magnetohydrodynamic (MHD) plasma phenomena such as the global magnetic-field generation, turbulence suppression, etc. Despite its relevance to the cross-helicity evolution, little attention has been paid to the dissipation rate of the turbulent cross helicity, $ε_W$. In this paper, we consider the model expression for the dissipation rate of the turbulent cross helicity. In addition to the algebraic model, an evolution equation of $ε_…
The dissipation of kinetic and magnetic energy in the interstellar medium (ISM) can proceed through viscous, Ohmic or ambipolar diffusion (AD). It occurs at very small scales compared to the scales at which energy is presumed to be injected. This localized heating may impact the ISM evolution but also its chemistry, thus providing observable features. Here, we perform 3D spectral simulations of decaying magnetohydrodynamic turbulence including the effects of AD. We find that the AD heating power spectrum peaks at scales in the inertial range, due to a strong alignment of the magnetic and curre…
Interstellar gas clouds are often both highly magnetized and supersonically turbulent, with velocity dispersions set by a competition between driving and dissipation. This balance has been studied extensively in the context of gases with constant mean density. However, many astrophysical systems are contracting under the influence of external pressure or gravity, and the balance between driving and dissipation in a contracting, magnetized medium has yet to be studied. In this paper we present three-dimensional (3D) magnetohydrodynamic (MHD) simulations of compression in a turbulent, magnetized…
We study the nature of pressure-strain interaction at reconnection sites, detected by NASA's Magnetospheric Multiscale (MMS) Mission. We employ data from a series of published case studies, including a large-scale reconnection event at the magnetopause, three small-scale reconnection events at the magnetosheath current sheets, and one example of the recently discovered electron-only reconnection. In all instances, we find that the pressure-strain shows signature of conversion into (or from) internal energy at the reconnection site. The electron heating rate is larger than the ion heating rate …
Kelvin's Theorem on conservation of circulations is an essential ingredient of G. I. Taylor's theory of turbulent energy dissipation by the process of vortex-line stretching. In previous work, we have proposed a nonlinear mechanism for the breakdown of Kelvin's Theorem in ideal turbulence at infinite Reynolds number. We develop here a detailed physical theory of this ``cascade of circulations''. Our analysis is based upon an effective equation for large-scale ``coarse-grained'' velocity, which contains a turbulent-induced ``vortex-force'' that can violate Kelvin's Theorem. We show that singula…
The ratio of ion to electron heating due to the dissipation of Alfvenic turbulence in astrophysical plasmas is calculated based on a cascade model for turbulence in weakly collisional plasmas. Conditions for validity of this model are discussed, a prescription for the turbulent heating is presented, and it is applied to predict turbulent heating in accretion disks and the interstellar medium.
We perform direct numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time to simulate the dynamics of a transverse section of a solar coronal loop. A stationary and large-scale magnetic forcing was imposed, to model the photospheric motions at the magnetic loop footpoints. A turbulent stationary regime is reached, which corresponds to energy dissipation rates consistent with the heating requirements of coronal loops. The temporal behavior of quantities such as the energy dissipation rate show clear indications of intermittency, whi…
Context: Recent satellite measurements in the turbulent magnetosheath of Earth have given evidence of an unusual reconnection mechanism that is driven exclusively by electrons. This newly observed process was called electron-only reconnection, and its inter-play with plasma turbulence is a matter of great debate. Aims: By using 2D-3V hybrid Vlasov-Maxwell simulations of freely decaying plasma turbulence, we study the role of electron-only reconnection in the development of plasma turbulence. In particular, we search for possible differences with respect to the turbulence associated with standa…
In this letter we report on turbulent acceleration of the dissipation of magnetic field in the postshock re- gion of a Poynting flux-dominated flow, such as the Crab pulsar wind nebula. We have performed two- dimensional resistive relativistic magnetohydrodynamics simulations of subsonic turbulence driven by the Richtmyer-Meshkov instability at the shock fronts of the Poynting flux-dominated flows in pulsar winds. We find that turbulence stretches current sheets which substantially enhances the dissipation of magnetic field, and that most of the initial magnetic field energy is dissipated with…
In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimen…
In the context of space and astrophysical plasma turbulence and particle heating, several vocabularies emerge for estimating turbulent energy dissipation rate, including Kolmogorov-Yaglom third-order law and, in its various forms, $\boldsymbol{j}\cdot\boldsymbol{E}$ (work done by the electromagnetic field on particles), and $-\left( \boldsymbol{P} \cdot \nabla \right) \cdot \boldsymbol{u}$ (pressure-strain interaction), to name a couple. It is now understood that these energy transfer channels, to some extent, are correlated with coherent structures. In particular, we find that different energ…
Characterization of Numerical Dissipation in Simulations of Magnetohydrodynamic Turbulence
Center for Applied Physics and Technology, HEDPS and SKLNPT, School of Physics, Peking University（北京大学物理学院，应用物理与技术中心，HEDPS和SKLNPT）；Frontiers Science Center for Nano-optoelectronics, Peking University（北京大学纳米光电前沿科学中心）
