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.

References

The questions are, how strong possible asymmetries are due to the nonlinearity and/or due to the new nonlocal term of the $\alpha$ effect or whether they may cancel each other.

— Oscillating dynamo models with a time-nonlocal $α$ effect  (2609.18933 - Rüdiger et al., 16 Sep 2026) in Section 4.1, subsection “Waldmeier profiles”

Determining whether such regimes can lead to growing modes requires a stability analysis including dissipative effects and nonlinear feedbacks.

— alpha_theta waves in the tachoclines of Sun-like stars  (2608.21183 - Zaqarashvili et al., 21 Aug 2026) in Section 4, Discussion