Nonmodal growth in magnetohydrodynamic shear flows with stabilizing magnetic fields

Shear flows are common and important in astrophysical and fusion plasmas, where they often drive fluctuations and turbulence. In turn, these motions enhance momentum, energy, and particle transport, crucially affecting the evolution of the system. The parameter boundaries delineating shear-driven fluctuations are often assumed to be adequately provided by normal-mode linear stability analyses. However, such analyses are known to be misleading in many canonical fluid systems, including pipe flow and stratified shear flows. Perturbations can undergo significant nonmodal or non-normal growth, in some cases driving turbulence and mixing even at parameters where linear stability analyses predict no growth. Here, we explore the degree of nonmodal growth when equilibrium magnetic fields aligned with the flow nearly or entirely stabilize shear flows, and show epsilon-pseudospectra that indicate significant amplification in linearly stable regimes for 2D systems. We also present the linear optimal perturbations that maximize fluctuation growth over finite times, and discuss how the growth and optimal perturbation structure varies with Reynolds number and magnetic field strength.