**Previous
abstract** **Next
abstract**

**Session 69 - The Solar Dynamo and Helioseismology.**

*Display session, Thursday, June 13*

*Tripp Commons, *

## [69.01] A Nonlinear Solar Dynamo Model With Variable \alpha and ømega Effects

*C. B. Roald, J. H. Thomas (U. Rochester)*
In the usual \alpha ømega dynamo, runaway growth of the
magnetic field is prevented by introducing arbitrary
quenching factors. These roughly represent the back-reaction
of the magnetic field on the flow by multiplying \alpha
and ømega by some decreasing function of the mean
toroidal magnetic field strength. This approach, while
straightforward, has only limited physical justification.
Here we take an alternate approach by allowing \alpha or
ømega to vary with latitude and time and derive dynamical
equations for them using principles of energy conservation.
The resulting system of nonlinear
partial differential equations is approximated by a
truncated Fourier-Galerkin expansion, leading to a system
of nonlinear ordinary differential equations whose behavior
is studied using the methods of nonlinear dynamical systems.
The results show that low-order truncations of the system
give misleading results, but at higher orders the system
converges to give consistent behavior, independent of
truncation order. Somewhat surprisingly, the results depend
strongly on which effect we choose to make dynamically
variable. The back-reaction on ømega appears to be far
more important in reproducing Sun-like dynamo oscillations.

**Program
listing for Thursday**