Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids

Exact relations for energy transfer in simple and active binary fluid turbulence

Inertial range energy transfer in three-dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two-point statistics, exact relations corresponding to the energy cascade are derived in terms of (i) two-point increments and (ii) two-point correlators. Despite having some apparent resemblances, the exact relation in binary fluid turbulence is found to be different from that of the incompressible magnetohydrodynamic turbulence [H. Politano and A. Pouquet, Geophys. Res. Lett. 25, 273 (1998)]0094-827610.1029/97GL03642. Besides the usual direct cascade of energy, under certain situations, an inverse cascade of energy is also speculated depending upon the strength of the activity parameter and the interplay between the two-point increments of the fluid velocity and the composition gradient fields. An alternative form of the exact relation is also derived in terms of the "upsilon" variables and a subsequent phenomenology is proposed predicting a k^{-3/2} law for the turbulent energy spectrum.

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities

We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two-fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.

Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory

The first complete estimation of the compressible energy cascade rate |ϵ_{C}| at magnetohydrodynamic (MHD) and subion scales is obtained in Earth's magnetosheath using Magnetospheric MultiScale spacecraft data and an exact law derived recently for compressible Hall MHD turbulence. A multispacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, |ϵ_{C}| identifies well with its incompressible analog |ϵ_{I}| at MHD scales but becomes much larger than |ϵ_{I}| at subion scales. For larger density fluctuations, |ϵ_{C}| is larger than |ϵ_{I}| at every scale with a value significantly higher than for smaller density fluctuations. Our study reveals also that for both small and large density fluctuations, the nonflux terms remain always negligible with respect to the flux terms and that the major contribution to |ϵ_{C}| at subion scales comes from the compressible Hall flux.

Determination of energy flux rate in homogeneous ferrohydrodynamic turbulence using two-point statistics

Under the influence of an external magnetic field H, the suspended ferromagnetic particles of a laminar ferrofluid flow try to be oriented along H through a relaxation mechanism. Turbulence affects the interaction between the magnetization of each suspended particle and the external field thereby leading to a large relaxation time and hence a slow relaxation process. This can be obtained by replacing viscous drag force with turbulent drag force in Brownian motion. We show that the total energy is an inviscid invariant in turbulent ferrofluids. Using two-point statistics we formulate an exact relation in the inertial zone of incompressible ferrofluid turbulence. This exact relation gives an accurate measure of the energy dissipation rate in a turbulent ferrofluid. We also show that (u×ω), (M×H), (M·∇)H, and (ω×M) play the major role in energy cascading in turbulent ferrofluids.