Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence

TL;DR

This paper investigates fluctuation energy as a key measure of gyrokinetic turbulence, expanding on prior work to analyze how energy transfer constraints influence turbulence behavior using multiple methods.

Contribution

It broadens the scope of previous findings by providing detailed analysis and additional methods to demonstrate the role of fluctuation energy constraints in gyrokinetic turbulence.

Findings

Spectral energy transfer is governed by fluctuation energy constraints.

Constrained transfer influences turbulence dynamics.

Fluctuation energies can predict turbulence behavior.

Abstract

In gyrokinetic theory there are two quadratic measures of fluctuation energy, left invariant under nonlinear interactions, that constrain the turbulence. The recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported on the novel consequences that this constraint has on the direction and locality of spectral energy transfer. This paper builds on that work. We provide detailed analysis in support of the results of Plunk and Tatsuno but also significantly broaden the scope and use additional methods to address the problem of energy transfer. The perspective taken here is that the fluctuation energies are not merely formal invariants of an idealized model (two-dimensional gyrokinetics) but are general measures of gyrokinetic turbulence, i.e. quantities that can be used to predict the behavior of the turbulence. Though many open questions remain, this paper collects evidence in favor of this perspective by demonstrating in several contexts that constrained spectral energy transfer governs the dynamics.