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

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.

Selected by the editors of Physics of Plasmas as a Featured article. https://doi.org/10.1063/5.0156560

References in corpus (6)

• Slowing the Spins of Stellar Cores
• The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
• Energy transfer in compressible magnetohydrodynamic turbulence
• The energetic coupling of scales in gyrokinetic plasma turbulence
• Angular momentum transport by the GSF instability: nonlinear simulations at the equator
• Near-cancellation of up- and down-gradient momentum transport in forced magnetized shear-flow turbulence