IMPACT OF NUMERICAL SIMULATIONS ON THE DESIGN OF
EXPERIMENTAL FLUID DYNAMOS
J. Léorat
Observatoire de Paris, Place Janssen, 92195- Meudon
France
e-mail : jacques.leorat@obspm.fr
ABSTRACT
There is no sufficient condition telling that a given flow is able to generate magnetic energy through dynamo action and theoretical predictions concerning the Earth magnetic reversals or the period of stellar magnetic activity are also lacking. The main tool to study either kinematic dynamos (linear regime) or nonlinear MHD turbulence is thus numerical computation. This field was indeed present among the main applications of computer science in its childhood, more than fifty years ago and it remains inescapable today. We shall present a short account of its role in designing experimental fluid dynamos.
Note first that the Lowes-Wilkinson experiment (1963), which represents the first experimental homogeneous dynamo (using solid iron) was built as a model of the theoretical Herzenberg dynamo, without help of numerical computations. At that time, the main objective of dynamo studies ( kinematic) was still to prove the feasibility of dynamo action against anti-dynamo theorems using arbitrary flows. Magnetic Reynolds numbers (Rm) were severely constrained by the lack of computer memory. In the case of experimental designs, the reduction of the critical magnetic Reynolds number ( Rmc) remains the main challenge, in order to keep the needed driving mechanical power below a few hundred kilowatts.
In a working dynamo, the conducting fluid is bounded by a container surrounded by an insulating medium, where Maxwell equations apply. In a bounded conductor, the magnetic boundary conditions (i.e. continuity of the tangential magnetic and electric fields) are simple only for spherical geometry. A conductivity jump between the fluid and its solid envelope offers an opportunity to reduce Rmc, but it represents also a source of numerical problems. It happens that adding such envelopes may lead to opposite effects when used either on the curved wall or on the flat lids [1].
Up to now, only two experimental facilities have produced dynamo action in a fluid (liquid sodium) , in Riga and in Karlsruhe, both in November 1999. They have quite different designs, but both have a cylindrical geometry, internal walls and Rmc of the order of 50, which was obtained after careful optimization of the flow, using numerical simulations which proved to predict Rmc close to the observed ones [2, 3].
Other experiments at large Rm are now progress using a torus ( Perm, Russia)) , spheres (Madison and Maryland, United States) or a cylinder (Cadarache, France), accompanied by simulations (see [4] for example). The objective of this new generation of experimental facilities is to avoid internal walls in order to reach a non linear regime closer to the one of natural dynamos. Non linear dynamo codes are highly welcome for optimization of these projects.
REFERENCES
[1] F. Stefani, M. Xu, G. Gerbeth, F. Ravelet, A. Chiffaudel, F. Daviaud and J. Léorat. “Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment”. European Journal of Mechanics B In press (2006).
[2] A. Tilgner, Physics Letters A226, 75, 1997; R. Stieglitz and U. Müller “Experimental demonstration of a homogeneous two-scale dynamo”, Phys. Fluids 13,561-564 (2001)
