Modeling Kinematic Dynamos in 2 and 3-D Ryan Horton, Nicholas - - PowerPoint PPT Presentation

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Modeling Kinematic Dynamos in 2 and 3-D Ryan Horton, Nicholas - - PowerPoint PPT Presentation

Mar 19, 2023 41 likes •243 views

Modeling Kinematic Dynamos in 2 and 3-D Ryan Horton, Nicholas Featherstone, Mark Miesch Motivation Convection on many di fg erent scales Magnetic events on many di fg erent scales Long (~22 year) solar cycle How do

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SLIDE 1

Modeling Kinematic Dynamos in 2 and 3-D

Ryan Horton, Nicholas Featherstone, Mark Miesch

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SLIDE 2

Motivation

  • Convection on many

difgerent scales

  • Magnetic events on many

difgerent scales

  • Long (~22 year) solar cycle
  • How do all these difgerent scales fit

together?

  • How can we know how accurately our

models are working?

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SLIDE 3

The Dynamic Sun Convection on Many Scales

SDO/AIA

Granulation Supergranulation

SST

Helioseismic Inference

Ω

360 nHz 500 nHz

Howe et al. 2000; Schou et al. 2002

Tachocline NSSL

Zhao et al. 2012 Meridional Circulation Difgerential Rotation

vθ

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SLIDE 4

\

Solar Cycle (The Big Mystery)

Lites et al (2008)

The Magnetic Sun

Small-Scale Magnetism (Magnetic Carpet) Global-Scale Magnetism

SDO/HMI

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SLIDE 5

The Induction Equation

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Advection (Movement) Always zero Compression and Expansion Stretching and Shear Generation Dissipation

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SLIDE 6

Magnetic Reynolds Number

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Generation Dissipation

  • Ratio of generation to dissipation
  • Essentially the reciprocal of the diffusivity
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SLIDE 7

Methods

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  • Numerical solution to induction equation
  • Periodic 3-D domain

Magneato

  • Computational domain broken up into many

small cubes

  • Constrained transport (Evans & Hawley 1988)
  • Preserves divergence free magnetic field by

integrating EMF around cell faces

EMF 1 EMF 2 dA 2 d A 1 B2 B 1

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SLIDE 8

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Examine the dynamo properties

  • f “solar-like” convective flows

Featherstone et al. 2009 Some examples of flows in current solar models

Objectives

Evans and Hawley 1988 There is always diffusion present

Assessing Dynamo Properties

  • f Numerical Difgusion
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SLIDE 9

Efgects of Vortical Flows in 2-D

  • Flow “winds up” the field
  • Takes field in one direction and

generates field in another direction

  • Eventually dissipation always wins as

fields in opposing directions come together

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Mofgatt 1978

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Code Validation

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The Expulsion of Magnetic Fields by Eddies, Weiss 1966

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SLIDE 11

Assessing Numerical Difgusion

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5e-7 5e-6 5e-5 5e-4 1000 400 200 100 40 Runs with Different Eta (128x128) Average Field Strength

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Magnetic Reynolds Number Peak of Average Magnetic Energy

32x32 64x64 128x128 ~Rm^(1/3)

Magnetic Reynolds Number vs Peak of Magnetic Field for Different Grid Spacings

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“2.5-D” Flow

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  • Invariant in z-direction
  • Vortices do not connect

Into Slide Out of Slide

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Magnetic Reynolds Number Peak Magnetic Energy

256x256 128x128

Different Grid Spacings with 2.5-D Flow

~Rm^(1/3) ~Rm^(1/3)

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Creating a Dynamo

  • Impossible in 2-D (difgusion always wins)
  • Field lines will wrap
  • Opposing field comes together and

cancels

  • Possible in 3-D
  • “stretch, twist, fold”

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SLIDE 16

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A-flow B-flow

Total flow is a weighted sum of the two

Fully 3-D Flow

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SLIDE 17

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Magnetic Energy Field Lines

128 Cubed 3-D Flow

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SLIDE 18

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Magnetic Energy Field Lines

After Many Iterations...

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SLIDE 19

Fully 3-D Dynamo

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Iterations (*25) M a g n e t i c E n e r g y

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SLIDE 20
  • Characterized numerical difgusion in two

and three dimensional flows

  • Showed that the numerical difgusion

depended on grid size

  • Showed the numerical difgusion varied

with flow

  • Creation of a 3-D dynamo motivated by

those flows present in solar models

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Overview