Nonlinear alpha(2)Omega-dynamo waves in stellar shells

Nonlinear alpha (2)Omega -dynamo waves are considered in a thin turbulent, differentially rotating convective stellar shell. Nonlinearity arises from cu-quenching, while an asymptotic solution is based on the small aspect rat io of the shell. Wave modulation is linked to a latitudinal-dependent local cu-effect and zonal shear flow magnetic Reynolds numbers R(alpha)f(theta) and R(Omega)g(theta) respectively; here B is the latitude. The study is a d irect extension of that of Meunier et al. (1997) for alpha Omega -dynamo wa ves which corresponds to finite dynamo number R alpha R Omega in the limit R alpha --> 0. The essential picture developed is that of a modulated dynamo wave whose am plitude varies spatially with theta. The linear solution is controlled by t he properties of the double turning point B, of the ordinary differential e quation for the mode amplitude. Significantly, though B, is real and is loc ated at the local dynamo number maximum in the alpha Omega -dynamo limit R- alpha --> 0, it migrates into the complex theta -plane once R-alpha not equ al 0. Linear and weakly nonlinear solutions are found over a limited range of R, and their qualitative properties are found to be largely similar to t hose for the alpha Omega -dynamo limit. One significant astrophysical diffe rence is the fact that the frequency generally decreases with increasing R- alpha. Thus alpha (2)Omega -stellar dynamos may occur with alpha Omega -dyn amo wave characteristics but exhibit significantly longer cycle times incre ased by a factor roughly two or more. Finite amplitude dynamo waves, like those when R-alpha --> 0, are modulated by an envelope which evaporates smoothly at some low latitude but is termi nated abruptly by a front at a high latitude BF Significantly, for given no n-zero R,, these frontal solutions are subcritical (a property linked to th e complex-value taken by B,). For sufficiently large R,, however, new low f requency modes emerge that are more closely related to steady alpha (2)-dyn amos localised near the pole theta = pi /2. In these circumstances, up to f our distinct finite amplitude states are identified; they may be loosely ch aracterised as alpha Omega -high frequency, alpha (2)Omega -medium frequenc y, alpha (2)-low frequency and alpha (2)-steady modes. In view of the possi ble mode competition, we comment on the likely realise physical state.