The field, the mean and the meaning
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The field, the mean and the meaning book
This chapter presents the fundamentals of mean field dynamo theory, with an emphasis on the statistical aspects of the theory. Mean field dynamo theory seems to have a controversial status. An important point to realise is that transport theory for mean quantities is a statistical theory. The equations for the mean are obtained by taking an average, and this has the unavoidable consequence that the predictive character of the equations disappears. The inexorable consequence of making an average is that the resulting equation for the mean has lost its predictive character. Failure to recognize the probabilistic aspects of the theory leads to paradoxical results, and that may be partly responsible for its controversial status. The chapter analyses the physics of turbulent diffusion and the information content of the dynamo equation, and argues that transport equations for the mean can only make probabilistic statements about the physical systems to which they apply.