### Abstract

The equation (δ_{t} + u•∇)C = R(x, t)C + κ∇^{2}C, is a scalar analogue of the magnetic induction equation. If the velocity field u(x, t) and the 'stretching' function R(x, t) are explicitly given, then we have the analogue of the dynamo problem. The scalar problem displays many of the same features as the vector kinematic dynamo problem. The fastest growing modes have growth rates that approach a finite limit as K→0 while the eigenfunctions develop more and more complex structure at smaller and smaller length scales. Some insight is provided by an analysis which finds a lower bound on the growth rate that is asymptotically independent of the diffusivity

Original language | English (US) |
---|---|

Pages (from-to) | 61-74 |

Number of pages | 14 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 73 |

Issue number | 1-4 |

State | Published - 1993 |

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### Keywords

- Fast dynamos

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Mechanics of Materials
- Computational Mechanics
- Astronomy and Astrophysics

### Cite this

*Geophysical and Astrophysical Fluid Dynamics*,

*73*(1-4), 61-74.

**Scalar dynamo models.** / Bayly, Bruce J.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 73, no. 1-4, pp. 61-74.

}

TY - JOUR

T1 - Scalar dynamo models

AU - Bayly, Bruce J

PY - 1993

Y1 - 1993

N2 - The equation (δt + u•∇)C = R(x, t)C + κ∇2C, is a scalar analogue of the magnetic induction equation. If the velocity field u(x, t) and the 'stretching' function R(x, t) are explicitly given, then we have the analogue of the dynamo problem. The scalar problem displays many of the same features as the vector kinematic dynamo problem. The fastest growing modes have growth rates that approach a finite limit as K→0 while the eigenfunctions develop more and more complex structure at smaller and smaller length scales. Some insight is provided by an analysis which finds a lower bound on the growth rate that is asymptotically independent of the diffusivity

AB - The equation (δt + u•∇)C = R(x, t)C + κ∇2C, is a scalar analogue of the magnetic induction equation. If the velocity field u(x, t) and the 'stretching' function R(x, t) are explicitly given, then we have the analogue of the dynamo problem. The scalar problem displays many of the same features as the vector kinematic dynamo problem. The fastest growing modes have growth rates that approach a finite limit as K→0 while the eigenfunctions develop more and more complex structure at smaller and smaller length scales. Some insight is provided by an analysis which finds a lower bound on the growth rate that is asymptotically independent of the diffusivity

KW - Fast dynamos

UR - http://www.scopus.com/inward/record.url?scp=0013102445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013102445&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0013102445

VL - 73

SP - 61

EP - 74

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 1-4

ER -