Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

TL;DR

This paper investigates how eigenmode interactions influence the saturation of 2D magnetized shear-flow turbulence, revealing the significant role of stable modes in energy transfer and turbulence dynamics.

Contribution

It introduces a novel eigenmode-based energy transfer analysis and a quasilinear model that isolates the impact of stable modes on turbulence saturation.

Findings

Stable modes reroute energy at the instability scale.

Enhanced turbulence and spectral energy fluxes observed.

Small-scale dissipation length-scale is reduced.

Abstract

To comprehensively understand saturation of two-dimensional ($2$D) magnetized Kelvin-Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasilinear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are: an explosive large-scale vortex separation instead of the well-known merger of $2$D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length-scale. These show critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.