Universal instability, non-modal amplification, and subcritical turbulence

The ``universal instability'' has been discounted since studies in 1978 found this drift wave to be absolutely stable for nonzero magnetic shear. We challenge this finding and demonstrate a variety of interesting behaviors in this sheared slab system: (1) The 1978 work was limited to $k \rho < 1$, but we show in gyrokinetics the linear mode with shear can be absolutely unstable for $k \rho > 1$ even with no temperature gradients, no trapped particles, and no magnetic curvature [1]. (2) Even if the system is linearly stable, significant transient linear amplification can occur [2]. Flow shear is unnecessary for this growth, in contrast to Navier-Stokes linear transients. (3) Turbulence can be sustained even if all linear eigenmodes are decaying [2], as seen previously in fluid models [3-4] and which we demonstrate kinetically. We generalize a Navier-Stokes proof [5] that transient linear amplification is required for sustained turbulence. While unstable eigenmodes are not necessary for sustained turbulence, a modified eigenvalue problem does provide a necessary condition [2].\\[4pt] [1] Landreman et al PRL 114, 095003 (2015).\\[0pt] [2] Landreman et al J Plasma Phys 81, 905810501 (2015).\\[0pt] [3] Scott, PRL 65, 3289 (1990).\\[0pt] [4] Drake et al, PRL 75, 4222 (1995).\\[0pt] [5] DelSole, J Atmos Sci 61, 1086 (2004).