An advanced visualization system for planetary dynamo simulations Moritz Heimpel 1, Pierre Boulanger 2, Curtis Badke 1, Farook Al-Shamali 1, Jonathan Aurnou 3 1 Institute for Geophysical Research, Department of Physics, University of Alberta 2 Department of Computing Sciences, University of Alberta 3 Department of Earth and Space Sciences, University of California, Los Angeles

Acknowledgements Acknowledgements Johannes Wicht (University of Goettingen) Ulrich Christensen (University of Goettingen) Gary Glatzmaier (University of California, Santa Cruz) Andreas Ritzer (University of Alberta) CNS and MACI (University of Alberta)

Some known dynamos Earth (  = 0.35) Mercury (  ~ 0.55?) Ganymede (  ~ ?) Io (  ~ ?) Jupiter (c ~ 0.85) Core radius ratio:  = r inner /r outer

Core geometry: The radius ratio  = r i /r o

Model geometry LEFT:  = 0.35 (Earth’s core); RIGHT:  = 0.75

Some non-dimensional parameters & typical values for our numerical simulations NumberDefinition Value Magnetic ReynoldsRm = VD/  Ekman numberE = /(  D 2 ) Rayleigh numberRa =  g o  TD 3 /(  ) Prandtl numberPr = /  Magnetic PrandtlPm =  Radius Ratio  = r i /r o 0.1 – 0.9

Spherical dynamo code Originally developed by G. Glatzmaier. Modified by U. Christensen and J. Wicht. We are presently running a slightly modified version of the Wicht code, called Magic2. Spectral transform code. Latitudinal and longitudinal directions expanded with spherical harmonics. Chebychev polynomials in radius. Time stepping via Courant criterion using a grid representation.

Critical Rayleigh number vs. radius ratio, 

Varying the radius ratio: Ra ~ Ra c  = 0.25  = 0.50  = 0.75

Number of Taylor Columns is proportional to the radius ratio

Varying the radius ratio: Ra = 5 Ra c  = 0.25  = 0.50  = 0.75

Critical Rayleigh number for dynamo action

Experimental Rotating Convection Cardin & Olson, 1992

Numerical dynamo:  = 0.35, E=10 -4, Pm = 1, Ra = 10Ra c

Real time visualization: Motivation Writing and storage of solutions more expensive than running simulation Interactive adjustment of run parameters can save calculation time Fast processing and data transfer makes real time feasible Visual immersion helps interpretation of dynamical structures.

data com Real time visualization: System architecture Dynamo Program N processors Solution server Stored solutions Visualisation Workstation Shared memory Solution 1 Solution 2 Solution 3. Solution m Solution formatter TCP/IP Fast Connection Initiate Simulation Control commands Server status Solution Parameters mallocdata com pthread

Single plume dynamo:  = 0.15, E = 10 -3, Ra = 2Ra c, Pm = 5, Energy time series

Single plume dynamo:  = 0.15, E = 10 -3, Ra = 2Ra c, Pm = 5, Dipole time series

Single plume dynamo: Movie of pole excursion, time steps, 1200 movie frames

Single Plume dynamo,  = 0.15 Temperature Isosurfaces Magnetic field lines Radial Magnetic Field at CMB

Numerical dynamo:  = 0.35, E = 10 -4, Pm = 1, Ra = 10Ra c

Real time visualization: Objectives Create a virtual sensory environment that helps the human brain to analyze numerical dynamos. – Bring the benefits of the experimental lab to the numerical laboratory Steering of numerical runs – Adjust parameters during a run – Adjust visualization tools (e.g. inject tracer particles) Independence of visualization system from computational code – Adaptation to various computational codes

Summary Variation of radius ratio could be a key for understanding the magnetic fields of planetary dynamos Dynamos of intermediate shell thickness are surprisingly Earth-like. Thick shell dynamos typically have single plume flow field. Thin shell dynamos have weaker dipole fields and are characterized by smaller scale flow and magnetic field scaling. Construction of real-time visualization system will aid interpretation of field structures.

Comparison of Earth magnetic field at CMB with dynamo model (U. Christensen et al., 1999)

The planetary dynamo problem The Earth’s magnetic field Spatial structure, an approximate dipole Time history, geomagnetic reversals Inversion for outer core flow structure Inner core differential rotation Planetary dynamos Origin and structure of magnetic fields

Three sets of model grids used to obtain Ra c  Symmetryr   l max fold fold full sphere

Steady dynamo: Vorticity, magnetic and velocity fields  = 0.55 Ra = 2 Rac E = 3 x 10-4 P = 1 Pm = 5

Steady Dynamo: Various visualizations a) Vorticity isosurfaces & velocity streamlines b) Volume vorticity & magnetic fieldlines c) Velocity magnitude d) Z - magnetic field ab cd

Equations of Motion

Some non-dimensional numbers & values for the Earth

Determining Critical Rayleigh, Ra Crit Nonmagnetic rotating convection Critical Rayleigh where KE > 0 Ra Crit decreases with increasing radius ratio, 

Presentation Outline Planetary dynamos Core geometry: the radius ratio Critical Rayleigh Number – For rotating convection – For dynamo action Simulation examples Real-time visualization