ON THE ROLE OF STAGNATION POINTS AND PERIODIC PARTICLE PATHS IN A 2-DIMENSIONAL PULSED FLOW FAST DYNAMO MODEL

The amplification of the magnetic field in an electrically conducting fluid by the dynamo action caused by a two-dimensional spatially perio dic flow consisting of two distinct Beltrami waves pulsed successively for time cu can be reduced to the study of the map of the field over the complete temporal period 2 alpha of the flow. The resulting eigenv alue problem has a largest eigenvalue which tends to a well-defined va lue in the perfect conductivity limit. The eigenfunction, on the other hand, has no limiting form and only exists as a generalised function characterised by its Fourier coefficients. To understand certain singu lar features of its structure, attention is restricted here to the par ticle paths, which move an integer multiple of the periodicity length during each pulse. In the limit alpha-->infinity, the positions of the se particles at any instant are dense, signalling strong chaos. The lo cal behaviour of the magnetic field in the neighborhood of them is dis cussed. The main result is the demonstration that the local algebraic singularities of the magnetic field in the vicinity of the stagnation points of the flow correspond to the high harmonics of the generalised eigenfunction. The implication of the result to the case of large but finite electrical conductivity is discussed.