Alice Courvoisier ,   University of Leeds

  
In the framework of kinematic dynamo theory we calculate the alpha-effect for two different
z-independent chaotic flows periodic in space and time,
namely the Galloway-Proctor flow (1992) and the MW+ flow (Otani 1993).
Two different methods are used. First we compute monochromatic magnetic field solutions
of the form H(x,y,k,t) exp(p(k)t+ikz) and evaluate the alpha-effect by computing
the limit of the k-dependent alpha-tensor as k tends to zero.
Then we also solve the induction equation for a z-independent field
and impose a mean-field Bo in the x-direction to evaluate the alpha-effect.
These methods are related in the sense that the second method corresponds to solving the induction equation
for a monochromatic solution to 0th order in k (Roberts 1970).
They show reasonnable agreement for low magnetic Reynold number Rm (~<30)
whereas for higher Rm only the 2nd method seems reliable as it prooves harder to reach the asymptotic regime for small k.
In addition some fully nonlinear calculations were performed using the 2nd method and varying the strength
of the imposed mean-field Bo.
Results show that the alpha-effect is quenched in an Rm-dependent
way while sometimes displaying an unexpected behaviour as Bo is varied.