K.-H. Rädler and A. Brandenburg
Remarks on kinetic helicity, -effect and dynamo action
Time: October 29, 2003, 3:00 pm
Place: Building 19, Room 19.415
The relevance of kinetic helicity of a flow of an electrically conducting fluid for dynamo action is discussed.
All dynamo mechanisms revealed by mean-field dynamo theory require some deviation of the small-scale motion from reflectional symmetry. In the simple case of isotropic turbulence an -effect and thus the possibility of a dynamo occurs if, in the high-conductivity limit, the averaged kinetic helicity is non-zero. This result is often overinterpreted in the sense that is the crucial quantity for any -effect dynamo or even any mean-field dynamo. However, in the case of an anisotropic turbulence and thus an anisotropic -effect it is no longer exactly this but some related quantity which is of interest for dynamo action. For isotropic turbulence and low-conductivity limit the -effect is proportional to , where is a vector potential of , and in special cases may well be non-zero even if vanishes. Apart from this, there are mean-field dynamos without any -effect, e.g., due to a combination of an electromotive force proportional to , resulting from some anisotropic turbulence, with a differential rotation, where is an axial vector, e.g., the angular velocity of the rotation. Such dynamos as well as related ones work even if is equal to zero.
These results support the now well known finding that also dynamos in the general sense (`laminar dynamos') are well possible if the kinetic helicity vanishes everywhere. Some examples for that are given. In this context also a few comments concerning the geodynamo mechanism are made.
Particular attention is focused on the Roberts dynamo as it has been realized in the Karlsruhe dynamo experiment. For the original Roberts flow, and so in the experiment, is non-zero. It has been shown both analytically and numerically that the dynamo works with modified flows, too, for which vanishes everywhere.