Download Stretch, Twist, Fold: The Fast Dynamo (Lecture Notes in by Stephen Childress PDF
By Stephen Childress
The learn of planetary or sun magnetic fields explains traditional magnetism as a phenomenon of magnetohydrodynamics. The kinematic dynamo idea, in particular the quick dynamo handled during this quantity, is slightly easier yet nonetheless it provides ambitious analytical difficulties relating to chaotic dynamics, for instance. This striking booklet offers the prestige of the idea, together with ideas of numerical simulations and modelling, in addition to a precis of effects to this point. the 1st 3 chapters introduce the matter and current examples of quickly dynamo motion in flows and maps. the remainder 9 chapters take care of numerous analytical methods and version structures. The booklet addresses astronomers and geophysicists, researchers and scholars alike.
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Extra resources for Stretch, Twist, Fold: The Fast Dynamo (Lecture Notes in Physics Monographs)
Sample text
We stress at once that few of these questions have been answered satisfactorily, and then only for very restrictive models. advective time-scale. In the case of the induction equation the diffusion time is L 2 1'TJ' In the present problem such usage would imply that some dynamos defined here as 'slow' would qualify as 'fast'. In a practical sense the distinction between a fast dynamo and a slow dynamo with, say, , rv II log E, is not essential. But it is worth indicating the origins of fast dynamo action in stretching flows by adopting the strict time-scale of the fluid, namely L I U.
6 we look at examples of three-dimensional steady flows. 2 Numerical Evidence for a Fast Dynamo in Otani's MW + Flow 33 view of dynamos, or even as dynamical systems (but see Feingold, Kadanoff & Piro 1988). Other possibilities include the random two- or three-dimensional flows studied in Chap. 11. 1 3 We call this the MW+ flow for brevity, meaning 'modulated waves, positive parity'. 14 Otani's modulation is one of many that might be considered by assigning general amplitudes a(t) and (3(t) to the waves, and so parameterising an oriented closed curve in the (a, (3)-plane.
7) We run the code until the fastest growing magnetic field eigenmode emerges and the growth rate settles down to ,(E, k). The solid line in Fig. 4. 4. 8. 8 and in Fig. 2 plot ,(E, k) against logiO liE. 39. From the computational evidence, the dynamo appears to be fast (Otani 1988, 1993). 2) for ,(E), can only increase the growth rate. 8 in Fig. 2, the corresponding eigenfunctions become wild in this limit. Fig. 3 shows eigenfunctions for decreasing values of E. We plot Re bx (x, y) at time t == 401r on a color scale with yellow I red for 36 2.