Non-axisymmetric vertical shear and convective instabilities as a mechanism of angular momentum transport

Discs and atmospheres with rotation profiles that depend on radius and height are subject to an axisymmetric linear instability (i.e. vertical shear instability). Here, we show that non-axisymmetric perturbations, while eventually stabilized, can sustain huge exponential amplifications with a growth rate close to the axisymmetric one. Therefore, transient growths are, in effect, genuine instabilities. The ensuing angular momentum transport is positive. These growths occur when the product of the radial times the vertical wavenumbers (both evolving with time) is positive for a positive local vertical shear, or negative for a negative local vertical shear. We have also studied the interaction between these growths induced by vertical shear and a convective instability. The asymptotic behaviour depends on the relative strength of the axisymmetric vertical shear (s(vs)) and convective (s(c)) growth rates. For s(vs) > s(c), we have observed the same type of behaviour as described above (i.e. large growths occur with asymptotic stabilization). When s(c) > s(vs), the system is asymptotically unstable, with a growth rate that can be slightly enhanced with respect to sc. The most interesting feature is the sign of the angular momentum transport. This is always positive in the phase in which the transient growths driven by vertical shear occur, even when s(c) > s(vs). We find that thermal diffusion has a stabilizing influence on the convective instability, especially for short wavelengths.