Griffiths, GL and Bassom, AP and Soward, AM and Kuzanyan, KM, Nonlinear2Ω-dynamowaves in stellarshells, Geophysical and Astrophysical Fluid Dynamics, 94, (1-2) pp. 85-133. ISSN 0309-1929 (2001) [Refereed Article]
Nonlinear α2Ω-dynamowaves are considered in a thin turbulent, differentially rotating convective stellarshell. Nonlinearity arises from α-quenching, while an asymptotic solution is based on the small aspect ratio of the shell. Wave modulation is linked to a latitudinal-dependent local α-effect and zonal shear flow magnetic Reynolds numbers Rαf(θ) and RΩg(θ) respectively; here θ is the latitude. The study is a direct extension of that of Meunier et al. (1997) for αΩ-dynamowaves which corresponds to finite dynamo number Rα RΩ in the limit Rα → O. The essential picture developed is that of a modulated dynamowave whose amplitude varies spatially with θ. The linear solution is controlled by the properties of the double turning point θc of the ordinary differential equation for the mode amplitude. Significantly, though θc is real and is located at the local dynamo number maximum in the αΩ-dynamo limit Rα → O, it migrates into the complex θ-plane once Rα ≠ O. Linear and weakly nonlinear solutions are found over a limited range of Rα and their qualitative properties are found to be largely similar to those for the αΩ-dynamo limit. One significant astrophysical difference is the fact that the frequency generally decreases with increasing Rα. Thus α2Ω-stellardynamos may occur with αΩ-dynamowave characteristics but exhibit significantly longer cycle times increased by a factor roughly two or more. Finite amplitude dynamowaves, like those when Rα → O, are modulated by an envelope which evaporates smoothly at some low latitude but is terminated abruptly by a front at a high latitude θF. Significantly, for given non-zero Rα, these frontal solutions are subcritical (a property linked to the complex-value taken by θc). For sufficiently large Rα, however, new low frequency modes emerge that are more closely related to steady α2-dynamos localised near the pole θ = θ/2. In these circumstances, up to four distinct finite amplitude states are identified; they may be loosely characterised as αΩ-high frequency, α2Ω-medium frequency, α2-low frequency and α2-steady modes. In view of the possible mode competition, we comment on the likely realised physical state.