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Method to Measure Tone of Axial and Proximal Muscle
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Kinematic dynamo action in square and hexagonal patterns.

B Favier1, M R E Proctor1

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
PubMed
Summary
This summary is machine-generated.

Kinematic dynamo action in rotating Boussinesq convection depends on flow patterns. Square patterns show large-scale dynamo at onset, while hexagonal patterns can suppress mean-field dynamos due to flow asymmetry.

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Area of Science:

  • Geophysics
  • Astrophysics
  • Fluid Dynamics

Background:

  • Investigating kinematic dynamo action in rapidly rotating Boussinesq convection.
  • Focusing on the regime just above the onset of convection.
  • Considering constrained velocity patterns: square and hexagonal.

Purpose of the Study:

  • To analyze the impact of different flow patterns on large-scale and small-scale dynamo action.
  • To understand the role of symmetry breaking in hexagonal convection.
  • To examine dynamo properties at varying rotation rates and magnetic Reynolds numbers.

Main Methods:

  • Numerical simulations of kinematic dynamo action.
  • Constraining fluid velocity to square and hexagonal patterns.
  • Varying magnetic Reynolds number and rotation rates.

Main Results:

  • Square patterns exhibit large-scale dynamo action at onset, with energy in the horizontally averaged component.
  • Increasing magnetic Reynolds number allows small-scale dynamo action, reducing the overall growth rate.
  • Hexagonal patterns, due to symmetry breaking, can generate a pumping velocity that inhibits mean-field dynamos at intermediate rotation rates.
  • At very high rotation rates, this pumping effect diminishes, making square and hexagonal patterns' dynamo properties similar.

Conclusions:

  • Flow geometry significantly influences dynamo action in rotating convection.
  • Symmetry breaking in hexagonal convection plays a crucial role in dynamo regimes.
  • Both large-scale and small-scale dynamos are possible, with their dominance depending on flow pattern and parameters.