On the convective overstability in protoplanetary discs

TL;DR

This paper investigates the convective overstability in protoplanetary disc dead zones, analyzing its linear theory, nonlinear solutions, and potential to generate turbulence, vortices, or zonal flows, with implications for disc dynamics.

Contribution

It revisits the linear theory of convective overstability, explores its nonlinear solutions, and discusses possible saturation mechanisms affecting disc turbulence and structure.

Findings

Unstable modes are exact nonlinear solutions in the local Boussinesq limit.

Secondary parametric instability limits mode growth, reducing turbulence strength.

Alternative saturation routes may produce zonal flows or layers in discs.

Abstract

This paper explores the driving of low-level hydrodynamical activity in protoplanetary-disc dead zones. A small adverse radial entropy gradient, ordinarily stabilised by rotation, excites oscillatory convection (`convective overstability') when thermal diffusion, or cooling, is neither too strong nor too weak. I revisit the linear theory of the instability, discuss its prevalence in protoplanetary discs, and show that unstable modes are exact nonlinear solutions in the local Boussinesq limit. Overstable modes cannot grow indefinitely, however, as they are subject to a secondary parametric instability that limits their amplitudes to relatively low levels. If parasites set the saturation level of the ensuing turbulence then the convective overstability is probably too weak to drive significant angular momentum transport or to generate vortices. But I also discuss an alternative, and far more vigorous, saturation route that generates radial `layers' or `zonal flows' (witnessed also in semiconvection). Numerical simulations are required to determine which outcome is favoured in realistic discs, and consequently how important the instability is for disc dynamics.