Note on the scalar dynamo model
作者:
R. Kaiser,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1996)
卷期:
Volume 82,
issue 1-2
页码: 125-135
ISSN:0309-1929
年代: 1996
DOI:10.1080/03091929608213632
出版商: Taylor & Francis Group
关键词: Fast dynamo;scalar dynamo model
数据来源: Taylor
摘要:
Bayly (1993) introduced and investigated the equation (ϑt+v·▽-η ▽2)S=RSas a scalar analogue of the magnetic induction equation. Here,S(r,t) is a scalar function and the flow fieldv(r,t) and “stretching” functionR(r,t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.
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