Turbulence, magnetism, and shear in stellar interiors

Annual Review of Fluid Mechanics

Volumn 41, Issue , 2009, Pages 317-345

  Miesch, Mark S ^a   Toomre, Juri ^b  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Differential rotation; Dynamo cycles; Magnetic dynamo; Stars; Sun; Turbulent convection

Indexed keywords

ASTROPHYSICAL FLUID DYNAMICS; CONTINUOUS OBSERVATION; DIFFERENTIAL ROTATION; DYNAMO CYCLES; HELIOSEISMOLOGY; INTERIOR DYNAMICS; MAGNETIC ACTIVITY; MAGNETIC DYNAMO; MERIDIONAL FLOWS; NEW HIGH; NON-LINEAR CONDITIONS; ROTATION RATE; ROTATIONAL SHEAR; SOLAR OSCILLATIONS; STELLAR INTERIOR; THREE-DIMENSIONAL NUMERICAL SIMULATIONS; TURBULENT CONVECTION;

COMPUTER SIMULATION LANGUAGES; ELECTRIC GENERATORS; HEAT CONVECTION; INTERACTIVE DEVICES; MAGNETISM; STARS; TURBULENCE;

ROTATION;

ASTRONOMY; CONVECTION; SEISMOLOGY; TURBULENCE;

EID: 67651052546     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fluid.010908.165215     Document Type: Review

References (140)

1. Alexakis A, Mininni PD, Pouquet A. 2006. On the inverse cascade of magnetic helicity. Astrophys. J. 640:335-43
2. Babcock HW. 1961. The topology of the Sun's magnetic field and the 22-year cycle. Astrophys. J. 133:572-87
3. Baliunas SL, Donahue RA, Soon WH, Home JH, Frazer J, et al. 1995. Chromospheric variations in main-sequence stars. II. Astrophys. J. 438:269-87
4. Baliunas SL, Nesme-Ribes E, Sololoff D, Soon WH. 1996. A dynamo interpretation of stellar activity cycles. Astrophys. J. 460:848-54
5. Ballot J, Brun AS, Turck-Chièze S. 2007. Simulations of turbulent convection in rotating young solar-like stars: differential rotation and meridional circulation. Astrophys. J. 669:1190-208
6. Berger MA, Field GB. 1984. The topological properties of magnetic helicity. J. Fluid Mech. 147:133-48
7. Biskamp D. 2003. Magnetohydrodynamic Turbulence. Cambridge: Cambridge Univ. Press. 297 pp.
8. Blackman EG, Brandenburg A. 2003. Doubly helical coronal ejections from dynamos and their role in sustaining the solar cycle. Astrophys. J. 584:L99-102
9. Blackman EG, Field GB. 2001. How astrophysical mean field dynamos can circumvent existing quenching constraints. Phys. Plasmas 8:2407-14
10. Brandenburg A. 2001. The inverse cascade and nonlinear a-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550:824-40
11. Brandenburg A. 2005. The case for a distributed dynamo shaped by near-surface shear. Astrophys. J. 625:539-47
12. Brandenburg A, Jennings RL, Nordlund A, Rieutord M, Stein RF, Tuominen I. 1996. Magnetic structures in a dynamo simulation. J. Fluid Mech. 306:325-52
13. Brandenburg A, Sandin C. 2004. Catastrophic alpha quenching alleviated by helicity flux and shear. Astron. Astrophys. 427:13-21
14. Brandenburg A, Subramanian K. 2005. Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417:1-209
15. Braun DC, Fan Y. 1998. Helioseismic measurements of the subsurface meridional flow. Astrophys. J. 508:L105-9
16. Brown BP, Browning MK, Brun AS, Miesch MS, Nelson NJ, Toomre J. 2007. Strong dynamo action in rapidly rotating suns. In Unsolved Problems in Stellar Physics, ed. RJ Stancliffe, G Houdek, RG Martin, CA Tout, pp. 271-78. AIP Conf. Proa, vol. 948. Melville, NY: Am. Inst. Phys.
17. Brown BP, Browning MK, Brun AS, Miesch MS, Toomre J. 2008. Active nests of convection in more rapidly rotating suns. Astrophys. J. In press
18. Browning MK. 2008. Simulations of dynamo action in fully convective stars. Astrophys. J. 676:1262-80
19. Browning MK, Brun AS, Miesch MS, Toomre J. 2007. Dynamo action in simulations of penetrative solar convection with an imposed tachocline. Astron. Nachr. 328:1100-3
20. Browning MK, Brun AS, Toomre J. 2004. Simulations of core convection in rotating A-type stars: differential rotation and overshooting. Astrophys. J. 601:512-29
21. Browning MK, Miesch MS, Brun AS, Toomre J. 2006. Dynamo action in the solar convection zone and tachocline: pumping and organization of toroidal fields. Astrophys. J. 648:L157-60
22. Brummell NH, Clune TL, Toomre J. 2002. Penetration and overshooting in turbulent compressible convection. Astrophys. J. 570:825-54
23. Brummell NH, Hurlburt NE, Toomre J. 1996. Turbulent compressible convection with rotation: I. Flow structure and evolution. Astrophys. J. 473:494-513
24. Brummell NH, Hurlburt NE, Toomre J. 1998. Turbulent compressible convection with rotation: II. Mean flows and differential rotation. Astrophys. J. 493:955-69
25. Brun AS, Browning MK, Toomre J. 2005. Simulations of core convection in rotating A-type stars: magnetic dynamo action. Astrophys. J. 629:461-81
26. Brun AS, Miesch MS, Toomre J. 2004. Global-scale turbulent convection and magnetic dynamo action in the solar envelope. Astrophys. J. 614:1073-98
27. Brun AS, Toomre J. 2002. Turbulent convection under the influence of rotation: sustaining a strong differential rotation. Astrophys. J. 570:865-85
28. Busse FH. 1970. Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44:441-60
29. Busse FH. 2002. Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14:1301-14
30. Canuto VM, Dubovikov M. 1998. Solar turbulent convection. I. Theory. Astrophys. J. 493:834-47
31. Canuto VM, Minotti FO, Schilling O. 1994. Differential rotation and turbulent convection: a new Reynolds stress model and comparison with solar data. Astrophys. J. 425:303-25
32. Carlsson M, Stein R E, Nordlund A, Scharmer GB. 2004. Observational manifestations of solar magnetocon-vection: center-to-limb variation. Astrophys. J. 610:L137-40
33. Cattaneo F, Brummell NH, Cline KS. 2006. What is a flux tube? On the magnetic field topology of buoyant flux structures. Mon. Not. R. Astron. Soc. 365:727-34
34. Cattaneo F, Brummell NH, Toomre J, Malagoli A, Hurlburt NE. 1991. Turbulent compressible convection. Astrophys. J. 370:282-94
35. Cattaneo F, Emonet T. 2003. On the interaction between convection and magnetic fields. Astrophys. J. 588:1183-98
36. Cattaneo F, Hughes DW. 1996. Nonlinear saturation of the turbulent α effect. Phys. Rev. E 54:4532-35
37. Cattaneo F, Hughes DW. 2006. Dynamo action in a rotating convective layer. J. Fluid Mech. 553:401-18
38. Chandrasekhar S. 1961. Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford Univ. Press. 652 pp.
39. Charbonneau P. 2005. Dynamo models of the solar cycle. Living Rev. Solar Phys. 2:lrsp-2005-2
40. Charbonneau P, MacGregor KB. 1996. On the generation of equipartition-strength magnetic fields by turbulent hydromagnetic dynamos. Astrophys. J. 473:L59-62
41. Charbonneau P, MacGregor KB. 1997. Solar interface dynamos. II. Linear, kinematic models in spherical geometry. Astrophys. J. 486:502-20
42. Cheung MCM, Schussler M, Moreno-Insertis F. 2007. Magnetic flux emergence in granular convection: radiative MHD simulations and observational signatures. Astron. Astrophys. 467:703-10
43. Christensen U, Aubert J. 2006. Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Int. 166:97-114
44. Christensen UR. 2002. Zonal flow driven by strongly supercritical convection in rotating spherical shells. J. Fluid Mech. 470:115-33
45. Christensen-Dalsgaard J, Gough DO, Thompson MJ. 1991. The depth of the solar convection zone. Astrophys. J. 378:413-37
46. Cline KS, Brummell NH, Cattaneo F. 2003. Dynamo action driven by shear and magnetic buoyancy. Astrophys. J. 599:1449-68
47. Clune TC, Elliott JR, Miesch MS, Toomre J, Glatzmaier GA. 1999. Computational aspects of a code to study rotating turbulent convection in spherical shells. Parallel Comput. 25:361-80
48. DeRosa ML, Gilman PA, Toomre J. 2002. Solar multiscale convection and rotation gradients studied in shallow spherical shells. Astrophys. J. 581:1356-74
49. DeRosa ML, Toomre J. 2004. Evolution of solar supergranulation. Astrophys. J. 616:1242-60
50. Diamond PH, Itoh SI, Itoh K, Silvers LJ. 2007. β-plane MHD turbulence and dissipation in the solar tachocline. See Hughes et al. 2007, pp. 213-39
51. Dikpati M, Charbonneau P. 1999. A Babcock-Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518:508-20
52. Dikpati M, Gilman PA. 2006. Simulating and predicting solar cycles using a flux-transport dynamo. Astrophys. J. 649:498-514
53. Dikpati M, Gilman PA, MacGregor KB. 2006. Constraints on the applicability of an interface dynamo to the Sun. Astrophys. J. 631:647-52
54. Dobler W, Stix M, Brandenburg A. 2006. Magnetic field generation in fully convective rotating spheres. Astrophys. J. 638:336-47
55. Durney BR. 1999. The Taylor-Proudman balance and the solar rotation data. Astrophys. J. 511:945-57
56. Durney BR, Spruit HC. 1979. On the dynamics of stellar convection zones: the effect of rotation on the turbulent viscosity and conductivity. Astrophys. J. 234:1067-78
57. Elliott JR, Miesch MS, Toomre J. 2000. Turbulent solar convection and its coupling with rotation: the effect of Prandtl number and thermal boundary conditions on the resulting differential rotation. Astrophys. J. 533:546-56
58. Emonet T, Cattaneo F. 2001. Small-scale photospheric fields: observational evidence and numerical simulations. Astrophys. J. 560:L197-200
59. Fan Y. 2004. Magnetic fields in the solar convection zone. Living Rev. Solar Phys. 1:lrsp-2004-1
60. Giles PM, Duvall TL, Scherrer PH, Bogart RS. 1997. A subsurface flow of material from the Sun's equator to its poles. Nature 390:52-54
61. Gilman PA. 1975. Linear simulations of Boussinesq convection in a deep rotating spherical shell. J. Atmos. Sci. 32:1331-52
62. Gilman PA. 1977. Nonlinear dynamics of Boussinesq convection in a deep rotating spherical shell I. Geophys. Astrophys. Fluid Dyn. 8:93-135
63. Gilman PA, Fox PA. 1997. Joint instability of latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J. 484:439-54
64. Gilman PA, Morrow CA, DeLuca EE. 1989. Angular momentum transport and dynamo action in the Sun: implications of recent oscillation measurements. Astrophys. J. 338:528-37
65. Gizon L, Birch AC. 2005. Local helioseismology. Living Rev. Solar Phys. 2:lrsp-2005-6
66. Glatzmaier GA, Gilman PA. 1981. Compressible convection in a rotating spherical shell. III. Analytic model for compressible vorticity waves. Astrophys. J. Suppl. 45:381-88
67. Gough DO, Kosovichev AG, Toomre J, Anderson E, Antia HM, et al. 1996. The seismic structure of the Sun. Science 272:1296-300
68. Gough DO, Mclntyre ME. 1998. Inevitability of a magnetic field in the Sun's radiative interior. Nature 394:755-57
69. Gough DO, Toomre J. 1991. Seismic observations of the solar interior. Annu. Rev. Astrcm. Astrophys. 29:627-84
70. Grote E, Busse FH, Tilgner A. 2000. Regular and chaotic spherical dynamos. Phys. Earth Planet. Int. 117:259-72
71. Gruzinov AV, Diamond PH. 1994. Self-consistent theory of mean-field electrodynamics. Phys. Rev. Lett. 72:1651-53
72. Haber DA, Hindman BW, Toomre J. 2002. Evolving submerged meridional circulation cells within the upper convection zone revealed by ring-diagram analysis. Astrophys. J. 570:855-64
73. Haber DA, Hindman BW, Toomre J, Thompson MJ. 2004. Organized subsurface flows near active regions. Solar Phys. 220:371-80
74. Hathaway DH. 1996. Doppler measurements of the Sun's meridional flow. Astrophys. J. 460:1027-33
75. Hathaway DH, Beck JG, Bogart RS, Bachmann KT, Khatri G, et al. 2000. The photospheric convection spectrum. Solar Phys. 193:299-312
76. Hindman BW, Gizon L, Duvall TL, Haber DA, Toomre J. 2004. Comparison of solar subsurface flows assessed by ring and time-distance analyses. Astrophys. J. 613:1253-62
77. Hindman BW, Haber DA, Toomre J. 2006. Helioseismically determined near-surface flows underlying a quiescent filamant. Astrophys. J. 653:725-32
78. Hughes DW. 2007. Magnetic buoyancy instabilities in the tachocline. See Hughes et al. 2007, pp. 275-98
79. Hughes DW, Rosner R, Weiss NO, eds. 2007. The Solar Tachocline. Cambridge: Cambridge Univ. Press. 367 pp.
80. Julien K, Legg S, McWilliams J, Werne J. 1996. Rapidly rotating turbulent Rayleigh-Bénard convection. J. Fluid Mech. 322:243-73
81. Kitchatinov LL, Rudiger G. 1993. A-effect and differential rotation in stellar convection zones. Astron. Astrophys. 276:96-102
82. Kitchatinov LL, Rüdiger G. 1995. Differential rotation in solar-type stars: revisiting the Taylor-number puzzle. Astron. Astrophys. 299:446-52
83. Komm R, Howe R, Hill F, Miesch M, Haber D, Hindman B. 2007. Divergence and vorticity of solar subsurface flows derived from ring-diagram analysis of MDI and GONG data. Astrophys. J. 667:571-84
84. KükerM, Rüdiger G. 2005. Differential rotation of main sequence F stars. Astron. Astrophys. 433:1023-30
85. Leighton RB. 1964. Transport of magnetic fields on the Sun. Astrophys. J. 140:1547-62
86. Lisle JP, Rast MP, Toomre J. 2004. Persistent north-south alignment of the solar supergranulation. Astrophys. J. 608:1167-74
87. Markiel JA, Thomas JH. 1999. Solar interface dynamo models with a realistic rotation profile. Astrophys. J. 523:827-37
88. Mclntyre ME. 1998. Breaking waves and global-scale chemical transport in the Earth's atmosphere, with spinoffs for the Sun's interior. Prog. Theor. Phys. Suppl. 130:137-66;
89. Corrigendum. Prog. Theor. Phys. 101:189
90. Mclntyre ME. 2007. Magnetic confinement and the sharp tachopause. See Hughes et al. 2007, pp. 183-212
91. Miesch MS. 2005. Large-scale dynamics of the convection zone and tachocline. Living Rev. Solar Phys. 2:lrsp-2005-1
92. Miesch MS. 2007. Differential rotation and meridional circulation in global models of solar convection. Astronom. Nachr. 328:998-1001
93. Miesch MS. 2008. Solar dynamo models. J. Phys. Conf. Ser. 118:012031
94. Miesch MS, Brun AS, DeRosa ML, Toomre J. 2008. Structure and evolution of giant cells in global models of solar convection. Astrophys. J. 673:557-75
95. Miesch MS, Brun AS, Toomre J. 2006. Solar differential rotation influenced by latitudinal entropy variations in the tachocline. Astrophys. J. 641:618-25
96. Miesch MS, Elliott JR, Toomre J, Clune TC, Glatzmaier GA, Gilman PA. 2000. Three-dimensional spherical simulations of solar convection: differential rotation and pattern evolution achieved with laminar and turbulent states. Astrophys. J. 532:593-615
97. Newcomb WA. 1961. Convective instability induced by gravity in a plasma with a frozen-in magnetic field. Phys. Fluids 4:391-96
98. Olah K. 2007. Changing stellar activity cycles. Astron. Nachr. 328:1072-74
99. Olson P, Christensen UR. 2006. Dipole moment scaling for convection-driven planetary dynamos. Earth Planet. Sci. Lett. 250:561-71
100. Ossendrijver M. 2003. The solar dynamo. Astron. Astrophys. Rev. 11:287-367
101. Palacios A, Brun AS. 2007. Simulation of turbulent convection in a slowly rotating red giant star. Astron. Nachr. 328:1114-17
102. Parker EN. 1993. A solar dynamo surface wave at the interface between convection and nonuniform rotation. Astrophys. J. 408:707-19
103. Petrovay K, Kerekes A. 2004. The effect of a meridional flow on Parker's interface dynamo. Mon. Not. R. Astron. Soc. 351:L59-62
104. Pouquet A, Frisch U, Léorat J. 1976. Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77:321-54
105. Rast MP, Ortiz A, Meisner RW. 2008. Latitudinal variation of the solar photospheric intensity. Astrophys. J. 673:1209-17
106. Rempel M. 2004. Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607:1046-64
107. Rempel M. 2005. Solar differential rotation and meridional flow: the role of a subadiabatic tachocline for the Taylor-Proudman balance. Astrophys. J. 622:1320-32
108. Rempel M. 2007. Transport of toroidal magnetic field by the meridional flow at the base of the solar convection zone. Astrophys. J. 637:1135-42
109. Rempel M. 2008. Solar and stellar activity cycles. J. Phys. Conf. Ser. 118:012032
110. Roberts PH, Glatzmaier GA. 2000. Geodynamo theory and simulations. Rev. Mod. Phys. 72:1081-123
111. Robinson FJ, Chan KL. 2001. A large-eddy simulation of turbulent compressible convection: Differential rotation in the solar convection zone. Mon. Not. R. Astron. Soc. 321:723-32
112. Rudiger G, Kitchatinov LL. 2007. Mean field modelling of differential rotation. See Hughes et al. 2007, pp. 129-44
113. Saar SH, Brandenburg A. 1999. Time evolution of the magnetic activity cycle period. II. Results for an expanded stellar sample. Astrophys. J. 524:295-310
114. Schou J, Antia HM, Basu S, Bogart RS, Bush RI, et al. 1998. Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson doppler imager. Astrophys. J. 505:390-417
115. Schrijver CJ, Zwaan C. 2000. Solar and Stellar Magnetic Activity. Cambridge: Cambridge Univ. Press. 384 pp.
116. Schussler M, Rempel M. 2005. The dynamical disconnection of sunspots from their magnetic roots. Astron. Astrophys. 441:337-46
117. Siggia ED. 1994. High Rayleigh number convection. Annu. Rev. Fluid Mech. 26:137-68
118. Solanki SK, Inhester B, Schüssler M. 2006. The solar magnetic field. Rep. Prog. Phys. 69:563-668
119. Spiegel EA, Zahn JP. 1992. The solar tachocline. Astron. Astrophys. 265:106-14
120. Spruit HC. 1999. Differential rotation and magnetic fields in stellar interiors. Astron. Astrophys. 349:189-202
121. Sreenivasan B, Jones CA. 2006. The role of inertia in the evolution of spherical dynamos. Geophys. J. Int. 164:467-76
122. Steffen M, Freytag B. 2007. Rotating star in a box experiments. Astron. Nachr. 328:1054-58
123. Stein RF, Nordlund A. 1998. Simulations of solar granulation: I. General properties. Astrophys. J. 499:914-33
124. Stein RF, Nordlund A. 2006. Solar small-scale magnetoconvection. Astrophys. J. 642:1246-55
125. Steiner O, Grossman-Doerth U, Kolker M, Schussler M. 1998. Dynamical interaction of solar magnetic elements and granular convection: results of a numerical simulation. Astrophys. J. 495:468-84
126. Talon S, Kumar P, Zahn JP. 2002. Angular momentum extraction by gravity waves in the Sun. Astrophys. J. 574:L175-78
127. Tassoul JL. 1978. Theory of Rotating Stars. Princeton: Princeton Univ. Press. 501 pp.
128. Thomas JH, Nye AH. 1975. Convective instability in the presence of a nonuniform horizontal magnetic field. Phys. Fluids 18:490-91
129. Thompson MJ, Christensen-Dalsgaard J, Miesch MS, Toomre J. 2003. The internal rotation of the Sun. Annu. Rev. Astran. Astrophys. 41:599-643
130. Tobias SM. 1998. Relating stellar cycle periods to dynamo calculations. Man. Not. R. Astron. Soc. 296:653-61
131. Tobias SM. 2005. The solar tachocline: formation, stability, and its role in the solar dynamo. In Fluid Dynamics and Dynamos in Astrophysics and Geophysics, ed. AM Soward, CA Jones, DW Hughes, NO Weiss, pp. 193-234. Oxford: Taylor & Francis
132. Tobias SM, Brummell NH, Clune TL, Toomre J. 2001. Transport and storage of magnetic field by overshooting turbulent compressible convection. Astrophys. J. 549:1183-203
133. Vögler A, Schüssler M. 2007. A solar surface dynamo. Astron. Astrophys. 465:L43-46
134. Vögler A, Shelyag S, SchüsslerM, Cattaneo F, Emonet T, Linde T. 2005. Simulations of magnto-convection in the solar photosphere: equations, methods, and results of the MURaM code. Astron. Astrophys. 429:335-51
135. Vorobieff P, Ecke RE. 1998. Vortex structure in rotating Rayleigh-Bénard convection. Rhys. D 123:153-60
136. Zahn JP. 1991. Convective penetration in stellar interiors. Astron. Astrophys. 252:179-88
137. Zhang K, Schubert G. 2000. Magnetohydrodynamics in rapidly rotating spherical systems. Annu. Rev. Astron. Astrophys. 32:409-43
138. Zhao J, Kosovichev AG. 2004. Torsional oscillation, meridional flows, and vorticity inferred in the upper convection zone of the Sun by time-distance helioseismology. Astrophys. J. 603:776-84
139. Zhou Q, Sun C, Xia KQ. 2007. Morphological evolution of thermal plumes in turbulent Rayleigh-Benard convection. Rhys. Rev. Lett. 98:074501
140. Ziegler U, Rüdiger G. 2003. Box simulations of rotating magnetoconvection: effects of penetration and turbulent pumping. Astron. Astrophys. 401:433-42