The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes

TL;DR

This study investigates how magnetic fields influence momentum transport and the saturation of shear-flow instability through stable modes in 2D magnetohydrodynamics, revealing that stronger fields suppress stable mode activity and alter energy cascades.

Contribution

It demonstrates the role of stable modes in momentum transport within magnetized shear flows and how magnetic field strength modulates their excitation and effects.

Findings

Stable modes transport momentum up its gradient, affecting layer width.

Weaker magnetic fields minimally affect linear instability but increase small-scale fluctuations.

Stronger magnetic fields reduce stable mode excitation, decreasing momentum transport and increasing energy dissipation.

Abstract

The Kelvin-Helmholtz (KH) instability of a shear layer with an initially-uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with KH-unstable flows in hydrodynamics, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the magnetic field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited and thus transport less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear due to stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not.