The fast kinematic magnetic dynamo and the dissipationless limit

Journal Article · Tue May 01 04:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859239· OSTI ID:7188389

Finn, J M; Ott, E ^[1]

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1. Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 (USA)

This paper investigates the possibility of utilizing the equation for the magnetic field in a {ital perfectly} {ital conducting} fluid to obtain information on the kinematic magnetic dynamo in the limit where the magnetic Reynolds number {ital R}{sub {ital m}} (equivalently, the conductivity) approaches infinity. Since the limit {ital R}{sub {ital m}}{r arrow}{infinity} is highly singular, it is not immediately clear that such an approach is possible. Recently, however, it has been proposed that the growth rate for the fastest growing mode at finite {ital R}{sub {ital m}}, {gamma}{sub max}({ital R}{sub {ital m}}), has a limit, {gamma}{sub {infinity}}=lim{sub {ital R}{sub {ital m}{r arrow}{infinity}}}{gamma}{sub max} ({ital R}{sub {ital m}}), which can be obtained directly from the flux through a macroscopic area, using the equation for the magnetic field in a perfectly conducting fluid. The utility of this is that it reduces the problem to one of investigating the chaotic dynamics of the trajectories of fluid elements convected by the flow. Numerical experiments with finite {ital R}{sub {ital m}} on a simple class of models will be presented. These numerical experiments support the idea that {gamma}{sub {infinity}} can be obtained from the perfect conductivity equation and elucidate the nature of the singular limiting process yielding this result.

• OSTI ID: 7188389
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:5; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

640430* -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY LOSSES
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY GROWTH RATES
LOSSES
MAGNETIC FIELDS
MAGNETIC REYNOLDS NUMBER
MAGNETOHYDRODYNAMICS
MECHANICS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
PLASMA
PLASMA SIMULATION
REYNOLDS NUMBER
SIMULATION
SINGULARITY