Nonlinear alpha-omega dynamos.

Shona Maclean ,  University of Glasgow

 We consider a non-linear axisymmetric mean-field $\alpha\omega$-dynamo model, where $\alpha$,
the parametrisation of the small-scale non-axisymmetric flow takes the form $\alpha=\alpha_o\cos\theta\sin(\pi(r-r_i))$.
$\Theta$, the parametrised buoyancy force is taken as $\Theta=-\Theta_o r\cos^2\theta$, such that it drives a differential rotation $\omega$ of the form $\omega=\Theta_o r$.
We solve the coupled system of equations in a spherical shell with a finitely conducting inner core,
 using a spectral method decomposition. Equilibration of the system is achieved through the non-linear
    Lorentz force in the momentum equation.
We investigate the effect of reversing the direction of the imposed buoyancy force and find that quadrupole
parity solutions are produced for $\Theta_o$ positive and dipole parity solutions for $\Theta_o$ negative.
Through fixing the magnitude of the buoyancy force, $\Theta_o$, we are able to find how the characteristics of the solutions change
    with increasing $\alpha_o$, and find very different behaviour depending on the sign of $\Theta_o$.
Even at the onset of dynamo action when the system is linear, we find that the system can not be defined by the product of $\alpha_o$ and $\Theta_o$ alone;
    these parameters must be specified separately as they are both important in characterising the types of solutions found.