Dynamo in fluctuating ABC - flow

The report considers influence of velocity field fluctuation on dynamo process. The dynamo process and the difficulties we face while its investigation are described. The concept of hydromagnetic dynamo (or otherwise the magnetic field self-excitation) process originated from attempts to explain the roots of the large-scale magnetic fields of celestial bodies. The main idea is as follows - motion of conducting medium exponentially amplifies a magnetic field which is initially weak.
This phenomenon usually appears in case of a natural random turbulence flow. However, well-established practice in physics forces scientists to find more ordinary field construction which can cause such a growth. It turns out that a geometrical (topological) structure of the flow plays the crucial role in magnetic field generation. For instance, Y.B. Zeldovich proved that dynamo was impossible for flows with streamlines which belong to a system of parallel planes. In this connection V.I. Arnold suggested to consider one of the fruitful possibilities of dynamo in a stationary chaotic flow. ABC-flow is the easiest example of such a flow. This flow is defined by three explicit formulas which include A, B, C coefficients it has been named after.
Researches which were perfomed in 1980s showed that, actually, there is the dynamo in this flow. However a structure of growing magnetic field differs from one appearing in turbulence flow. Y.B. Zeldovich assumed that it is a nonstationarity which is required from the ABC-flow to generate large-scale magnetic field. It looks reasonable to introduce this time-dependence in the ABC-flow. The specific implementation of this idea belongs to S.A.Molchanov. He suggested to assume coefficients A, B, C as short-correlated random processes. Further research progress required great number of calculation so it took a long time to be completed. Today the idea has been implemented and detailed investigations confirmed that Zeldovich's hypothesis was correct.