Freely decaying turbulence in two-dimensional electrostatic gyrokinetics

TL;DR

This paper investigates freely decaying two-dimensional electrostatic gyrokinetic turbulence, revealing dual cascades in phase space and deriving decay laws for different collisional regimes through theory and simulations.

Contribution

It introduces a comprehensive analysis of dual cascades and asymptotic states in 2D gyrokinetic turbulence, including new decay laws and the concept of a critical collisionality parameter.

Findings

Dual cascades observed in velocity and position space.

Turbulence evolves toward a single growing scale over time.

Identification of three regimes based on a dimensionless collisionality number D*.

Abstract

In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*.