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| Titel |
Statistical theory of dynamo |
| VerfasserIn |
E. Kim, A. P. Newton |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250069479
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| Zusammenfassung |
| One major problem in dynamo theory is the multi-scale nature of the MHD turbulence, which
requires statistical theory in terms of probability distribution functions. In this contribution,
we present the statistical theory of magnetic fields in a simplified mean field α-Ω dynamo
model by varying the statistical property of alpha, including marginal stability and
intermittency, and then utilize observational data of solar activity to fine-tune the mean field
dynamo model.
Specifically, we first present a comprehensive investigation into the effect of the
stochastic parameters in a simplified α-Ω dynamo model. Through considering
the manifold of marginal stability (the region of parameter space where the mean
growth rate is zero), we show that stochastic fluctuations are conductive to dynamo.
Furthermore, by considering the cases of fluctuating alpha that are periodic and Gaussian
coloured random noise with identical characteristic time-scales and fluctuating
amplitudes, we show that the transition to dynamo is significantly facilitated for stochastic
alpha with random noise. Furthermore, we show that probability density functions
(PDFs) of the growth-rate, magnetic field and magnetic energy can provide a wealth
of useful information regarding the dynamo behaviour/intermittency. Finally, the
precise statistical property of the dynamo such as temporal correlation and fluctuating
amplitude is found to be dependent on the distribution the fluctuations of stochastic
parameters.
We then use observations of solar activity to constrain parameters relating to the effect in
stochastic α-Ω nonlinear dynamo models. This is achieved through performing a
comprehensive statistical comparison by computing PDFs of solar activity from observations
and from our simulation of mean field dynamo model. The observational data that are used
are the time history of solar activity inferred for C14 data in the past 11000 years on a long
time scale and direct observations of the sun spot numbers obtained in recent years
1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to
obtain PDFs of the solar activity on both long and short time scales. These PDFs are then
compared with predicted PDFs from numerical simulation of our α-Ω dynamo model,
where α is assumed to have both mean α0 and fluctuating α′ parts. By varying the
correlation time of fluctuating α′, the ratio of the amplitude of the fluctuating to
mean alpha -¨α′2-©-α02 (where angular brackets -¨-© denote ensemble average), and
the ratio of poloidal to toroidal magnetic fields, we show that the results from our
stochastic dynamo model can match the PDFs of solar activity on both long and short
time scales. In particular, a good agreement is obtained when the fluctuation in
alpha is roughly equal to the mean part with a correlation time shorter than the solar
period. |
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