Anelastic Magnetohydrodynamic Equations for Modeling Solar and Stellar Convection Zones

Lantz, Steven; Fan, Yuhong

doi:10.1086/313187

Cited by 142 publications

(161 citation statements)

References 31 publications

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“…2 below). We also note that there is a difference in the definition of the reference atmosphere used in the present paper compared to that in Lantz & Fan (1999), which we describe in the Appendix.…”

Section: The Numerical Modelmentioning

confidence: 97%

“…The anelastic approximation is suitable for numerical simulations of subsonic, dynamic processes in the high-plasma of the solar (or stellar) interior. The detailed derivation of the anelastic MHD equations has been described elsewhere (see, e.g., Gilman & Glatzmaier 1981;Glatzmaier 1984;Lantz & Fan 1999). Here we directly list the anelastic equations, which we solve numerically:…”

Section: The Numerical Modelmentioning

confidence: 99%

“…PRESENT PAPER AND LANTZ & FAN (1999) In this appendix we clarify a difference in the definition of the reference atmosphere used in the present paper compared to that in Lantz & Fan (1999). In Lantz & Fan (1999), the reference atmosphere (denoted by T 0 , p 0 , 0 , and s 0 ) was defined to correspond strictly to the zero-order balance in the anelastic scaling, which is an adiabatically stratified equilibrium atmosphere, since to zero order, ds 0 =dz ¼ 0 or s 0 ¼ 0 (or any constant; see eq.…”

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

“…In Lantz & Fan (1999), the reference atmosphere (denoted by T 0 , p 0 , 0 , and s 0 ) was defined to correspond strictly to the zero-order balance in the anelastic scaling, which is an adiabatically stratified equilibrium atmosphere, since to zero order, ds 0 =dz ¼ 0 or s 0 ¼ 0 (or any constant; see eq.…”

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

“…[38] in Lantz & Fan 1999). A separate timeindependent, first-order Oð Þ entropy gradient ds d ðzÞ=dz called the '' drive function '' was then added (see eq.…”

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

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The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

Fan

Abbett

Fisher

2003

ApJ

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We present three-dimensional numerical simulations of the dynamic evolution of uniformly buoyant, twisted horizontal magnetic flux tubes in a three-dimensional stratified convective velocity field. Our calculations are relevant to understanding how stratified convection in the deep solar convection zone may affect the rise and the structure of buoyant flux tubes that are responsible for the emergence of solar active regions. We find that in order for the magnetic buoyancy force of the tube to dominate the hydrodynamic force due to the convective downflows, the field strength B of the flux tube needs to be greater than ðH p =aÞ 1=2 B eq $ 3B eq , where H p is the pressure scale height, a is the tube radius, and B eq is the field strength in equipartition with the kinetic energy density of the strong downdrafts. For tubes of equipartition field strength (B ¼ B eq ), the dynamic evolution depends sensitively on the local condition of the convective flow. Sections of the tube in the paths of strong downdrafts are pinned down to the bottom despite their buoyancy, while the rise speed of sections within upflow regions is significantly boosted; -shaped emerging tubes can form between downdrafts. Although flux tubes with B ¼ B eq are found to be severely distorted by convection, the degree of distortion obtained from our simulations is not severe enough to clearly rule out the -tubes that are able to emerge between downdrafts as possible progenitors of solar active regions. As the initial field strength of the tube becomes higher than the critical value of $ðH p =aÞ 1=2 B eq given above, the dynamic evolution converges toward the results of previous simulations of the buoyant rise of magnetic flux tubes in a static, adiabatically stratified model solar convection zone. Tubes with 10 times the equipartition field strength are found to rise unimpeded by the downdrafts and are not significantly distorted by the three-dimensional convective flow.

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Section: The Numerical Modelmentioning

confidence: 97%

Section: The Numerical Modelmentioning

confidence: 99%

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

“…[38] in Lantz & Fan 1999). A separate timeindependent, first-order Oð Þ entropy gradient ds d ðzÞ=dz called the '' drive function '' was then added (see eq.…”

Section: Appendix a Note On The Different Definitions Of The Referencmentioning

confidence: 99%

See 3 more Smart Citations

The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

Fan

Abbett

Fisher

2003

ApJ

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Explaining Jupiter's magnetic field and equatorial jet dynamics

Gastine

Wicht

Duarte

et al. 2014

Geophysical Research Letters

117

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Spacecraft data reveal a very Earth-like Jovian magnetic field. This is surprising since numerical simulations have shown that the vastly different interiors of terrestrial and gas planets can strongly affect the internal dynamo process. Here we present the first numerical dynamo that manages to match the structure and strength of the observed magnetic field by embracing the newest models for Jupiter's interior. Simulated dynamo action primarily occurs in the deep high electrical conductivity region while zonal flows are dynamically constrained to a strong equatorial jet in the outer envelope of low conductivity. Our model reproduces the structure and strength of the observed global magnetic field and predicts that secondary dynamo action associated to the equatorial jet produces banded magnetic features likely observable by the Juno mission. Secular variation in our model scales to about 2000 nT per year and should also be observable during the one year nominal mission duration.Comment: 7 pages, 4 figures, accepted for publication in Geophysical Research Letter

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Conservative integrals of adiabatic Durran's equations

Smolarkiewicz

Dörnbrack²

2007

Numerical Methods in Fluids

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SUMMARYPotential advances are investigated in the area of generalized anelastic approximations. Consistent controlvolume integrals are designed and compared for the established Lipps-Hemler form (of anelastic approximation) and Durran's pseudo-incompressible form. The Durran system provides a unique theoretical tool-useful for research of geophysical and stellar flows-within the existing set of reduced, Boussinesqtype fluid models. It represents thermal aspects of compressibility free of sound waves, yet the momentum equation is unapproximated. The latter admits unabbreviated baroclinic production of vorticity, thus facilitating separation of compressibility and baroclinicity effects per se. Compared with other reduced fluid models, there is little cumulative experience with integrating the Durran system. Perhaps the first conservative integrations of Durran's equations are presented, using flux-form transport methods and exact projection for the associated elliptic problem. Because the resulting code is built from a preexisting anelastic model, the consistency of the numerics is assured thus minimizing uncertainties associated with ad hoc code comparisons. While broader physical implications are addressed, theoretical considerations are illustrated with examples of atmospheric flows.

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Anelastic Magnetohydrodynamic Equations for Modeling Solar and Stellar Convection Zones

Cited by 142 publications

References 31 publications

The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

Explaining Jupiter's magnetic field and equatorial jet dynamics

Conservative integrals of adiabatic Durran's equations

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