Gyrokinetic Theory of Shear Stabilization of the Gravitational Interchange

Finite Larmor radius (FLR) effects are known to be stabilizing for large perpendicular wavenumber flute instabilities. For small wavenumbers, velocity shear can be introduced to assist in stabilization; however, the shear also acts to tilt the modes, thereby increasing its wavenumber from the perspective of the shearing frame. What results is a combined stabilizing effect from both FLR effects and shear. Moreover, even if the net effect results in no unstable modes, it is still possible for the mode to undergo linear transient amplification that can drive turbulence. Previously, shear stabilization of interchanges have been studied using the framework of MHD by Ng & Hassam (2005); however, this model is limited to small perpendicular wavenumbers, which does not hold under sustained shear. To fully capture the FLR effects in conjuction with the shear, we shall utilize the framework of Gyrokinetics (Abel et al. 2013) and the method previously utilized by Schekochihin et al. (2011) to study ITG and PVG instabilities in the presence of shear. Numerical comparisons between MHD and Gyrokinetics are made, as well as with a simulation from GX (Mandell et al. 2019, Mandell et al. 2024).