Turbulent Dynamics Under Two Ideal Invariants: Dynamic Phase Alignment in Plasmas and Nonionized Fluids

Abstract

Turbulent dynamics in the presence of two invariants is poorly understood in both plasmas and non-ionized fluids. The celebrated Kolmogorov model of turbulence considered energy as the only invariant of the system, but it was subsequently discovered that a second invariant exists, namely (generalized) helicity. We present results of numerical studies of turbulence in low-𝛽ₑ plasmas at scales below the electron skin depth and turbulence in non-ionized fluids governed by the Navier-Stokes equations. In both systems, the dynamics is dominated by the presence of energy and (generalized) helicity as two exact invariants. We show that, in the two systems, both invariants are subject to a forward cascade, and we demonstrate that this joint cascade is possible due to the existence of a strong dependence on scale of the Fourier phase alignment angle between, in low-𝛽ₑ plasmas, fluctuations of electric and magnetic potential and, in Navier-Stokes turbulence, fluctuations of velocity and vorticity. This phenomenon, termed dynamic phase alignment, thus acquires importance as a mechanism regulating the dynamics in the presence of two invariants, arising from their conservation in the joint direct cascade, regardless of the details of the physical interactions.

We further investigate the role of magnetic reconnection in the inverse transfer of magnetic energy in a low-𝛽, kinetic system. We show that the merging of magnetic islands into progressively larger structures can lead to energy being transferred from small to large scales within a model that captures finite electron skin depth and finite ion Larmor radius effects as well as Landau damping. We explore the effects of Landau damping and of the generation of plasmoids on the system dynamics.