No abstract

Exact laws for evaluating cascade rates, tracing back to the Kolmogorov “4/5” law, have been extended to many systems of interest including magnetohydrodynamics (MHD), and compressible flows of the magnetofluid and ordinary fluid types. It is understood that implementations may be limited by the quantity of available data and by the lack of turbulence symmetry. Assessment of the accuracy and feasibility of such third-order (or Yaglom) relations is most effectively accomplished by examining the von Kármán–Howarth equation in increment form, a framework from which the third-order laws are derived as asymptotic approximations. Using this approach, we examine the context of third-order laws for incompressible MHD in some detail. The simplest versions rely on the assumption of isotropy and the presence of a well-defined inertial range, while related procedures generalize the same idea to arbitrary rotational symmetries. Conditions for obtaining correct and accurate values of the dissipation rate from these laws based on several sampling and fitting strategies are investigated using results from simulations. The questions we address are of particular relevance to sampling of solar wind turbulence by one or more spacecraft.

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell (PIC) simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power law behavior, with a slope near -5/3 at wave numbers smaller than the inverse ion inertial length, and a slope steeper than -8/3 for larger wave numbers up to the inverse electron inertial length.This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70 degrees to about 48 degrees (nearly isotropic) by the end of the simulation.

Despite decades of study of high-temperature weakly collisional plasmas, a complete understanding of how energy is transferred between particles and fields in turbulent plasmas remains elusive. Two major questions in this regard are how fluid-scale energy transfer rates, associated with turbulence, connect with kinetic-scale dissipation, and what controls the fraction of dissipation on different charged species. Although the rate of cascade has long been recognized as a limiting factor in the heating rate at kinetic scales, there has not been direct evidence correlating the heating rate with MHD-scale cascade rates. Using kinetic simulations and in situ spacecraft data, we show that the fluid-scale energy flux indeed accounts for the total energy dissipated at kinetic scales. A phenomenology, based on disruption of proton gyromotion by fluctuating electric fields that are produced in turbulence at proton scales, argues that the proton versus electron heating is controlled by the ratio of the nonlinear timescale to the proton cyclotron time and by the plasma beta. The proposed scalings are supported by the simulations and observations.

<p>Over the past few decades, the relationship between turbulence and reconnection has emerged as a subject of interest. For example, various properties of reconnection have been studied in different turbulent environments using plasma simulations. In other approaches, reconnection is studied as a subsidiary process occurring in turbulence. Turbulent features are also studied as consequences of instabilities associated with large scale reconnection. Only recently, we have attempted to answer some of the fundamental questions such as: “What are the turbulent-like features of laminar magnetic reconnection?”, "Is magnetic reconnection fundamentally an energy cascade?" both related to the interplay between reconnection and turbulence. Using 2.5D particle in cell simulations, we have found that laminar magnetic reconnection in a quasi-steady phase exhibits a Kolmogorov-like power spectrum. Most notably, the energy transfer process in magnetic reconnection is also found to be similar to that of a turbulent system suggesting that reconnection involves an energy cascade. The reconnection rate is correlated to both the magnetic energy spectrum in the ion-scales and the cascade of energy. Further, similarities between reconnection and turbulence in terms of the electric field spectrum, their components, and pressure-strain interaction will be highlighted.</p>