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FOCUS ON RESEARCH: GEOPHYSICS & PLANETARY SCIENCES 
Convection and Magnetic Field Generation In Planets and Stars
Gary A. Glatzmaier, Professor
Tami Rogers, Martha Evonuk
Objectives
Global magnetic fields are observed on some terrestrial planets, on all of our giant planets and on the sun. Differential rotation is observed on the surfaces of giant planets and the sun and is inferred via helioseismology in the solar interior. The most dramatic displays of differential rotation exist on the surfaces of our gas giants, Jupiter and Saturn. These planets have a strong eastward jet in the equatorial region with weaker alternating westward and eastward jets at higher latitudes. The ice giants, Uranus and Neptune, are quite different; they have one broad jet centered on the equator and directed westward. The sun also has just one broad jet but it is eastward at the equator.
We are supported by NASA grants to study the magnetohydrodynamics of the interiors of the giant planets and the sun. We use computers at NASA, NSF and DOE supercomputer centers and a Beowulf cluster at UCSC to run the parallel codes we have developed that simulate the turbulent dynamics in the interiors of these bodies.
Approach
Our 3D model solves a coupled nonlinear system of equations that describes conservation of mass, momentum and energy and the induction of magnetic field. The solution is the 3D time-dependent fluid velocity, magnetic field, density, pressure, specific entropy, light constituent mass fraction and gravitational potential, all within the modeled rotating fluid sphere.
The model uses a spectral solution method (Glatzmaier, 1984), i.e., the variables are expanded in spherical harmonics to represent their horizontal structures and in Chebyshev polynomials to describe their radial structures. The nonlinear terms are computed in physical space using a spectral transform method (fast Fourier transforms). The solution is evolved in spectral space, treating the linear terms implicitly and the nonlinear terms explicitly.
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Figure 1: A snapshot from one of our geodynamo simulations. The magnetic field is displayed with a set of magnetic field lines; gold (blue) field lines represent outward (inward) directed field.
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Figure 2: A snapshot of the longitudinal flows of one of our 3D simulations of the internal dynamics of a giant planet. Yellows and reds represent eastward flows and blues represent westward flows (relative to the mean surface rotation). Like Saturn, there is a strong eastward jet in the equatorial region with alternating westward and eastward jets at higher latitudes.
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This model has been validated by simulating a rotating convection experiment flown on board NASA space shuttles in 1985 and 1995 (Hart, Glatzmaier, Toomre, 1986). The spectral method is very accurate; the challenge is to make the required global communication efficient on massively parallel machines. We usually run our code on 256 processors with a spatial resolution of 241 radial levels, 768 latitudinal levels and 768 longitudinal levels. At this resolution we can run with low enough viscous, thermal and magnetic diffusivities to just begin to simulate 3D turbulent convection. Thomas Clune (GSFC) has worked with the PI for many years improving the parallelization and efficiency of this code (Glatzmaier and Clune, 2000).
Scientific Accomplishments
This model produced the first computer simulation of compressible convection and magnetic field generation in the sun's convection zone, i.e., the solar dynamo (Glatzmaier, 1984). Another version of this model was used to produce the first simulation of convection and magnetic field generation in the Earth's fluid core, i.e., the geodynamo, including a series of spontaneous Earth-like magnetic field reversals (Glatzmaier and Roberts, 1995) and the prediction of the super-rotation of the Earth's solid inner core (Glatzmaier and Roberts, 1996). Figure 1 is a snapshot of the 3D structure of our simulated geomagnetic field, illustrated with magnetic field lines. |
During the the past couple years we have run simulations of the magnetohydrodynamics in the deep interior of a giant planet like Saturn. Figure 2 shows a snapshot of the longitudinal winds near the model's surface, which are maintained by the interactions of convection and the planetary rotation (Glatzmaier et al., 2006; Evonuk and Glatzmaier, 2006a,b). The strong eastward jet in the equatorial region and the alternating series of westward and eastward jets at higher latitudes agree well with the banded zonal winds observed on Saturn.
We have also produced the first high-resolution simulations of turbulent convection and gravity waves in the solar interior (Rogers and Glatzmaier, 2005, 2006a,b). The challenge is understand the interactions between gravity waves in the deep stable interior and convection in the outer unstable region (Figure 3) and the generation of magnetic field at the interface between these two regions.
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Figure 3: A snapshot of temperature in one of our simulations of turbulent convection and gravity waves in the equatorial plane of the sun.
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References
Evonuk, M. and Glatzmaier, G.A., ICARUS, 181, 458-464 (2006a).
Evonuk, M. and Glatzmaier, G.A., Planet. Space Sci., in press (2006b).
Glatzmaier, G.A., J. Comp. Phys., 55, 461-484 (1984).
Glatzmaier G.A. and Clune, T., Comput. Sci. Eng., 2, 61-67 (2000).
Glatzmaier, G.A., Evonuk, M. and Rogers, T.M., ICARUS, under review (2006).
Glatzmaier, G.A. and Roberts, P.H., Nature, 377, 203-209 (1995).
Glatzmaier, G.A. and Roberts, P.H., Science, 274, 1887-1891 (1996).
Hart, J.E., Glatzmaier, G.A. and Toomre, J., J. Fluid Mech., 173, 519-544 (1986).
Rogers, T.M. and Glatzmaier, G.A., Mon. Not. R. Astron. Soc., 364, 1135-1146 (2005).
Rogers, T.M. and Glatzmaier, G.A., Astrophys. J., in press (2006a).
Rogers, T.M. and Glatzmaier, G.A., Astrophys. J., in press (2006b).
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