Transient growth in magnetohydrodynamic shear layers

Shear flows are ubiquitous in astrophysical and fusion plasmas and can drive turbulent fluctuations that enhance momentum, heat, and particle transport. Normal-mode linear stability analyses are widely used to identify unstable parameter regimes that might drive such turbulence. However, these analyses are known to be misleading in many canonical fluid systems, including pipe flow and stratified shear flows. Even in the absence of linear instability, small-amplitude perturbations can grow significantly due to transient, nonmodal growth mechanisms. In some cases, they can even drive turbulence and significant mixing.

Here, we show that nonmodal growth remains significant in magnetized shear flows. We study a simple shear layer with a uniform magnetic field in the MHD limit. When the field is strong enough to suppress the Kelvin-Helmholtz (KH) instability, the same nonmodal effects that drive turbulence in neutral fluids also drive significant linear growth here. This growth increases dramatically in domains much larger than the typical KH lengthscale. This demonstrates that modal analyses can be misleading when used to assess stability of MHD shear flows and that simulations in small domains may miss crucial dynamics.