Stability of alpha-theta waves near critical latitudinal gradients

Determine whether regimes of alpha-theta waves near critical values of the latitudinal alpha-gradient can produce growing modes by incorporating dissipative effects and nonlinear feedbacks into the stability analysis.

Background

The paper derives alpha-theta waves generated by vertical and latitudinal gradients of the turbulent dynamo coefficient in the overshoot tachoclines of Sun-like stars. For negative latitudinal alpha-gradients, the wave frequency can approach zero at a critical gradient, causing the nominal wave period to become very large and signaling a transition between retrograde and prograde propagation.

The analysis is linear and omits dissipative effects and nonlinear feedbacks. Consequently, the authors do not establish whether the weak-restoring-force regime near the critical gradient is merely a neutral propagation transition or can support genuine instability and mode growth. A stability analysis with the omitted physical effects is therefore left unresolved.