1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 48, 2016
  5. Article

Annual Review of Fluid Mechanics

Volume 48, 2016

Seismic Sounding of Convection in the Sun

Abstract

Thermal convection is the dominant mechanism of energy transport in the outer envelope of the Sun (one-third by radius). It drives global fluid circulations and magnetic fields observed on the solar surface. Vigorous surface convection excites a broadband spectrum of acoustic waves that propagate within the interior and set up modal resonances. These acoustic waves, also called seismic waves in this context, are observed at the surface of the Sun by space- and ground-based telescopes. Seismic sounding, the study of these seismic waves to infer the internal properties of the Sun, constitutes helioseismology. Here we review our knowledge of solar convection, especially that obtained through seismic inference. Several characteristics of solar convection, such as differential rotation, anisotropic Reynolds stresses, the influence of rotation on convection, and supergranulation, are considered. On larger scales, several inferences suggest that convective velocities are substantially smaller than those predicted by theory and simulations. This discrepancy challenges the models of internal differential rotation that rely on convective stresses as a driving mechanism and provide an important benchmark for numerical simulations.

Keyword(s): heat transport, helioseismology, non-Boussinesq effects, turbulent convection
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-122414-034534
2016-01-03
2024-04-19
Loading full text...

Full text loading...

/deliver/fulltext/fluid/48/1/annurev-fluid-122414-034534.html?itemId=/content/journals/10.1146/annurev-fluid-122414-034534&mimeType=html&fmt=ahah

Literature Cited

  1. Adam J. 1977. Hydrodynamic instability of convectively unstable atmospheres in shear flow. Astrophys. Space Sci. 50:493–514 [Google Scholar]
  2. Ahlers G. 2009. Trend: turbulent convection. Physics 2:74 [Google Scholar]
  3. Ahlers G, He X, Funfschilling D, Bodenschatz E. 2012. Heat transport by turbulent Rayleigh–Bénard convection for Pr≃0.8 and 3×1012≲Ra≲1015: aspect ratio Γ = 0.50. New J. Phys. 14:103012 [Google Scholar]
  4. Alvan L, Brun AS, Mathis S. 2014. Theoretical seismology in 3D: nonlinear simulations of internal gravity waves in solar-like states. Astron. Astrophys. 565:A42 [Google Scholar]
  5. Balbus SA, Schaan E. 2012. The stability of stratified, rotating systems and the generation of vorticity in the Sun. Mon. Not. R. Astron. Soc. 426:1546–57 [Google Scholar]
  6. Barekat A, Schou J, Gizon L. 2014. The radial gradient of the near-surface shear layer of the Sun. Astron. Astrophys. 570:L12 [Google Scholar]
  7. Bessolaz N, Brun AS. 2011. Hunting for giant cells in deep stellar convective zones using wavelet analysis. Astrophys. J. 728:115 [Google Scholar]
  8. Birch AC, Duvall TL Jr, Gizon L, Jackiewicz J. 2006. Helioseismology of the “average” supergranule. Bull. Am. Astron. Soc. 38:224 [Google Scholar]
  9. Böhm-Vitense E. 1958. Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Z. Astrophys. 46:108–43 [Google Scholar]
  10. Braun DC, Birch AC, Lindsey C. 2004. Local helioseismology of near-surface flows. SOHO 14 Helio- and Asteroseismology: Towards a Golden Future D Danesy 337–40 Noordwijk, Neth: Eur. Space Agency [Google Scholar]
  11. Brun AS, Miesch MS, Toomre J. 2011. Modeling the dynamical coupling of solar convection with the radiative interior. Astrophys. J. 742:79 [Google Scholar]
  12. Busse FH. 2003. Drifting convection cells in rotating fluid layers heated from below. Phys. Rev. Lett. 91:244501 [Google Scholar]
  13. Busse FH. 2007. Convection in the presence of an inclined axis of rotation with applications to the sun. Sol. Phys. 245:27–36 [Google Scholar]
  14. Canuto VM, Dubovikov M. 1998. Stellar turbulent convection. I. Theory. Astrophys. J. 493:834–47 [Google Scholar]
  15. Castaing B, Gunaratne G, Heslot F, Kadanoff L, Libchaber A. et al. 1989. Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204:1–30 [Google Scholar]
  16. Chandrasekhar S. 1961. Hydrodynamic and Hydromagnetic Stability New York: Clarendon
  17. Chillà F, Schumacher J. 2012. New perspectives in turbulent Rayleigh-Bénard convection. Eur. Phys. J. E 35:58 [Google Scholar]
  18. Christensen-Dalsgaard J. 2002. Helioseismology. Rev. Mod. Phys. 74:1073–129 [Google Scholar]
  19. Christensen-Dalsgaard J, Dappen W, Ajukov SV, Anderson ER, Antia HM. et al. 1996. The current state of solar modeling. Science 272:1286–92 [Google Scholar]
  20. Christensen-Dalsgaard J, Monteiro MJPFG, Rempel M, Thompson MJ. 2011. A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology. Mon. Not. R. Astron. Soc. 414:1158–74 [Google Scholar]
  21. De Rosa M, Duvall TL Jr, Toomre J. 2000. Near-surface flow fields deduced using correlation tracking and time-distance analyses. Sol. Phys. 192:351–61 [Google Scholar]
  22. Dikpati M, Charbonneau P. 1999. A Babcock-Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518:508–20 [Google Scholar]
  23. Dombroski DE, Birch AC, Braun DC, Hanasoge SM. 2013. Testing helioseismic-holography inversions for supergranular flows using synthetic data. Sol. Phys. 282:361–78 [Google Scholar]
  24. Duvall TL Jr. 1980. The equatorial rotation rate of the supergranulation cells. Sol. Phys. 66:213–21 [Google Scholar]
  25. Duvall TL Jr. 2003. Nonaxisymmetric variations deep in the convection zone. GONG +2002. Local and Global Helioseismology: the Present and Future H Sawaya-Lacoste 259–62 Noordwijk, Neth: Eur. Space Agency [Google Scholar]
  26. Duvall TL Jr, Birch AC, Gizon L. 2006. Direct measurement of travel-time kernels for helioseismology. Astrophys. J. 646:553–59 [Google Scholar]
  27. Duvall TL Jr, Gizon L. 2000. Time-distance helioseismology with f modes as a method for measurement of near-surface flows. Sol. Phys. 192:177–91 [Google Scholar]
  28. Duvall TL Jr, Hanasoge SM. 2013. Subsurface supergranular vertical flows as measured using large distance separations in time-distance helioseismology. Sol. Phys. 287:71–83 [Google Scholar]
  29. Duvall TL Jr, Hanasoge SM, Chakraborty S. 2014. Additional evidence supporting a model of shallow, high-speed supergranulation. Sol. Phys. 289:3421–33 [Google Scholar]
  30. Duvall TL Jr, Jefferies SM, Harvey JW, Pomerantz MA. 1993. Time-distance helioseismology. Nature 362:430–32Introduces the method of time-distance helioseismology, widely used to image three-dimensional structures and flows in the solar interior. [Google Scholar]
  31. Ecke R, Niemela J. 2014. Heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 113:114301 [Google Scholar]
  32. Egorov P, Rüdiger G, Ziegler U. 2004. Vorticity and helicity of the solar supergranulation flow field. Astron. Astrophys. 425:725–28 [Google Scholar]
  33. Elliott JR, Gough DO. 1999. Calibration of the thickness of the solar tachocline. Astrophys. J. 516:475–81 [Google Scholar]
  34. Fournier D, Gizon L, Hohage T, Birch AC. 2014. Generalization of the noise model for time-distance helioseismology. Astron. Astrophys. 567:A137 [Google Scholar]
  35. Ghizaru M, Charbonneau P, Smolarkiewicz PK. 2010. Magnetic cycles in global large-eddy simulations of solar convection. Astrophys. J. Lett. 715:L133–37 [Google Scholar]
  36. Giles PM, Duvall TL Jr, Scherrer PH, Bogart RS. 1997. A flow of material from the Sun's equator to its poles. Nature 390:52–54 [Google Scholar]
  37. Gizon L. 2006. Probing convection and solar activity with local helioseismology. SOHO-17: 10 Years of SOHO and Beyond H Lacoste 1–8 Noordwijk, Neth: Eur. Space Agency [Google Scholar]
  38. Gizon L, Birch AC. 2002. Time-distance helioseismology: the forward problem for random distributed sources. Astrophys. J. 571:966–86 [Google Scholar]
  39. Gizon L, Birch AC. 2004. Time-distance helioseismology: noise estimation. Astrophys. J. 614:472–89 [Google Scholar]
  40. Gizon L, Birch AC. 2005. Local helioseismology. Living Rev. Sol. Phys. 2:6 [Google Scholar]
  41. Gizon L, Birch AC. 2012. Helioseismology challenges models of solar convection. PNAS 109:11896–97 [Google Scholar]
  42. Gizon L, Birch AC, Spruit HC. 2010. Local helioseismology: three-dimensional imaging of the solar interior. Annu. Rev. Astron. Astrophys. 48:289–338Summarizes methods and results of local helioseismology. [Google Scholar]
  43. Gizon L, Duvall TL Jr. 2003. Supergranulation supports waves. Proceedings of SOHO 12/GONG +2002: Local and Global Helioseismology; The Present and Future H Sawaya-Lacoste 43–52 Noordwijk, Neth: Eur. Space Agency
  44. Gizon L, Duvall TL Jr, Schou J. 2003. Wave-like properties of solar supergranulation. Nature 421:43–44 [Google Scholar]
  45. Graham JP, Cameron R, Schüssler M. 2010. Turbulent small-scale dynamo action in solar surface simulations. Astrophys. J. 714:1606–16 [Google Scholar]
  46. Greer BJ, Hindman BW, Featherstone NA, Toomre J. 2015. Helioseismic imaging of fast convective flows throughout the near-surface layer. Astrophys. J. Lett. 803:L17 [Google Scholar]
  47. Goldbaum N, Rast MP, Ermolli I, Sands JS, Berrilli F. 2009. The intensity profile of the solar supergranulation. Astrophys. J. 707:67–73 [Google Scholar]
  48. Goldreich P, Keeley DA. 1977. Solar seismology. II. The stochastic excitation of the solar p-modes by turbulent convection. Astrophys. J. 212:243–51 [Google Scholar]
  49. Gough DO. 1969. The anelastic approximation for thermal convection. J. Atmos. Sci. 26:448–56 [Google Scholar]
  50. Gough DO. 1977. Mixing-length theory for pulsating stars. Astrophys. J. 214:196–213 [Google Scholar]
  51. Grossmann S, Lohse D. 2000. Scaling in thermal convection: a unifying view. J. Fluid Mech. 407:27–56 [Google Scholar]
  52. Grossmann S, Lohse D. 2011. Multiple scaling in the ultimate regime of thermal convection. Phys. Fluids 23:045108 [Google Scholar]
  53. Hanasoge SM, Birch AC, Gizon L, Tromp J. 2012a. Seismic probes of solar interior magnetic structure. Phys. Rev. Lett. 109:101101 [Google Scholar]
  54. Hanasoge SM, Birch AC, Gizon L, Tromp J. 2011. The adjoint method applied to time-distance helioseismology. Astrophys. J. 738:100 [Google Scholar]
  55. Hanasoge SM, Duvall TL Jr, De Rosa ML. 2010. Seismic constraints on interior solar convection. Astrophys. J. Lett. 712:L98–102 [Google Scholar]
  56. Hanasoge SM, Duvall TL Jr, Sreenivasan KR. 2012b. Anomalously weak solar convection. PNAS 109:11928–32Bounds solar large-scale convective velocities, constraining them to be two orders of magnitude smaller than theory. [Google Scholar]
  57. Hanasoge SM, Gizon L, Bal G. 2013. Propagation of seismic waves through a spatio-temporally fluctuating medium: homogenization. Astrophys. J. 773:101 [Google Scholar]
  58. Hanasoge SM, Sreenivasan KR. 2014. The quest to understand supergranulation and large-scale convection in the sun. Sol. Phys. 289:3403–19 [Google Scholar]
  59. Hart AB. 1954. Motions in the Sun at the photospheric level. IV. The equatorial rotation and possible velocity fields in the photosphere. Mon. Not. R. Astron. Soc. 114:17–38 [Google Scholar]
  60. Hathaway DH, Beck J, Bogart R, Bachmann K, Khatri G. et al. 2000. The photospheric convection spectrum. Sol. Phys. 193:299–312 [Google Scholar]
  61. Hathaway DH, Upton L, Colegrove O. 2013. Giant convection cells found on the sun. Science 342:1217–19 [Google Scholar]
  62. Horn S, Shishkina O. 2015. Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J. Fluid Mech. 762:232–55 [Google Scholar]
  63. Hotta H, Rempel M, Yokoyama T. 2014. High-resolution calculations of the solar global convection with the reduced speed of sound technique. I. The structure of the convection and the magnetic field without the rotation. Astrophys. J. 786:24 [Google Scholar]
  64. Howe R. 2009. Solar interior rotation and its variation. Living Rev. Sol. Phys. 6:1 [Google Scholar]
  65. Howe R, Christensen-Dalsgaard J, Hill F, Komm RW, Larsen RM. et al. 2000. Dynamic variations at the base of the solar convection zone. Science 287:2456–60 [Google Scholar]
  66. Jackiewicz J, Birch AC, Gizon L, Hanasoge SM, Hohage T. et al. 2012. Multichannel three-dimensional SOLA inversion for local helioseismology. Sol. Phys. 276:19–33 [Google Scholar]
  67. Jackiewicz J, Gizon L, Birch AC. 2008. High-resolution mapping of flows in the solar interior: fully consistent OLA inversion of helioseismic travel times. Sol. Phys. 251:381–415 [Google Scholar]
  68. Jameson A. 1988. Aerodynamic design via control theory. J. Sci. Comput. 3:233–60 [Google Scholar]
  69. Käpylä PJ, Korpi MJ, Brandenburg A, Mitra D, Tavakol R. 2010. Convective dynamos in spherical wedge geometry. Astron. Nachr. 331:73–81 [Google Scholar]
  70. Käpylä PJ, Mantere MJ, Guerrero G, Brandenburg A, Chatterjee P. 2011. Reynolds stress and heat flux in spherical shell convection. Astron. Astrophys. 531:A162 [Google Scholar]
  71. Kitchatinov LL, Pipin VV, Rüdiger G. 1994. Turbulent viscosity, magnetic diffusivity, and heat conductivity under the influence of rotation and magnetic field. Astron. Nachr. 315:157–70 [Google Scholar]
  72. Kichatinov LL, Rüdiger G. 1993. Λ-effect and differential rotation in stellar convection zones. Astron. Astrophys. 276:96–102 [Google Scholar]
  73. Kitchatinov LL, Rüdiger G. 2005. Differential rotation and meridional flow in the solar convection zone and beneath. Astron. Nachr. 326:379–85 [Google Scholar]
  74. Kosovichev AG, Duvall TL Jr. 1997. Acoustic tomography of solar convective flows and structures. SCORe'96: Solar Convection and Oscillations and Their Relationship FP Pijpers, J Christensen-Dalsgaard, CS Rosenthal 241–60 New York: Springer [Google Scholar]
  75. Langfellner J, Gizon L, Birch AC. 2014. Time-distance helioseismology: a new averaging scheme for measuring flow vorticity. Astron. Astrophys. 570:A90 [Google Scholar]
  76. Langfellner J, Gizon L, Birch AC. 2015. Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking. Astron. Astrophys. 581A67
  77. Leibacher JW, Stein RF. 1971. A new description of the solar five-minute oscillation. Astrophys. Lett. 7:191–92 [Google Scholar]
  78. Leighton RB, Noyes RW, Simon GW. 1962. Velocity fields in the solar atmosphere. I. Preliminary report. Astrophys. J. 135:474–99 [Google Scholar]
  79. Lord JW, Cameron RH, Rast MP, Rempel M, Roudier T. 2014. The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows. Astrophys. J. 793:24 [Google Scholar]
  80. Lynden-Bell D, Ostriker JP. 1967. On the stability of differentially rotating bodies. Mon. Not. R. Astron. Soc. 136:293–310 [Google Scholar]
  81. Mathis S. 2013. Transport processes in stellar interiors. Studying Stellar Rotation and Convection: Theoretical Background and Seismic Diagnostics M Goupil, K Belkacem, C Neiner, F Lignières, JJ Green 23–47 Lect. Notes Phys. 865 Berlin: Springer-Verlag [Google Scholar]
  82. Meunier N, Tkaczuk R, Roudier T. 2007. Intensity variations inside supergranules. Astron. Astrophys. 463:745–53 [Google Scholar]
  83. Miesch MS. 2005. Large-scale dynamics of the convection zone and tachocline. Living Rev. Sol. Phys. 2:1Gives an overview of numerical simulations of solar convection. [Google Scholar]
  84. Miesch MS, Browning MK, Brun AS, Toomre J, Brown BP. 2009. Three-dimensional simulations of solar and stellar dynamos: the influence of a tachocline. Solar-Stellar Dynamos as Revealed by Helio- and Asteroseismology: GONG 2008/SOHO 21 M Dikpati, T Arentoft, I González Hernández, C Lindsey, F Hill 443–52 Orem, UT: Astron. Soc. Pac. [Google Scholar]
  85. Miesch MS, Brun AS, De Rosa ML, Toomre J. 2008. Structure and evolution of giant cells in global models of solar convection. Astrophys. J. 673:557–75 [Google Scholar]
  86. Miesch MS, Featherstone NA, Rempel M, Trampedach R. 2012. On the amplitude of convective velocities in the deep solar interior. Astrophys. J. 757:128 [Google Scholar]
  87. Miesch MS, Toomre J. 2009. Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41:317–45 [Google Scholar]
  88. Niemela JJ, Babuin S, Sreenivasan KR. 2010. Turbulent rotating convection at high Rayleigh and Taylor numbers. J. Fluid Mech. 649:509–22 [Google Scholar]
  89. Niemela JJ, Skrbek L, Sreenivasan KR, Donnelly R. 2000. Turbulent convection at very high Rayleigh numbers. Nature 404:837–40Presents convection experiments using liquid helium at extremely high Rayleigh numbers. [Google Scholar]
  90. Niemela JJ, Sreenivasan KR. 2003. Confined turbulent convection. J. Fluid Mech. 481:355–84 [Google Scholar]
  91. Niemela JJ, Sreenivasan KR. 2006a. Turbulent convection at high Rayleigh numbers and aspect ratio 4. J. Fluid Mech. 557:411–22 [Google Scholar]
  92. Niemela JJ, Sreenivasan KR. 2006b. The use of cryogenic helium for classical turbulence: promises and hurdles. J. Low Temp. Phys. 143:163–212 [Google Scholar]
  93. Niemela JJ, Sreenivasan KR. 2010. Does confined turbulent convection ever attain the ‘asymptotic scaling’ with 1/2 power?. New J. Phys. 12:115002 [Google Scholar]
  94. Nordlund Å, Stein RF, Asplund M. 2009. Solar surface convection. Living Rev. Sol. Phys. 6:2 [Google Scholar]
  95. Oresta P, Stringano G, Verzicco R. 2007. Transitional regimes and rotation effects in Rayleigh–Bénard convection in a slender cylindrical cell. Eur. J. Mech. B/Fluids 26:1–14 [Google Scholar]
  96. Prandtl L. 1925. Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech 5:136–39 [Google Scholar]
  97. Rast MP. 2003. The scales of granulation, mesogranulation, and supergranulation. Astrophys. J. 597:1200–10 [Google Scholar]
  98. Rempel M, Schüssler M, Knölker M. 2009. Radiative magnetohydrodynamic simulation of sunspot structure. Astrophys. J. 691:640–49 [Google Scholar]
  99. Rieutord M, Meunier N, Roudier T, Rondi S, Beigbeder F, Pares L. 2008. Solar supergranulation revealed by granule tracking. Astron. Astrophys. 479:L17–20 [Google Scholar]
  100. Rieutord M, Rincon F. 2010. The Sun's supergranulation. Living Rev. Sol. Phys. 7:2 [Google Scholar]
  101. Rieutord M, Roudier T, Rincon F, Malherbe JM, Meunier N. et al. 2010. On the power spectrum of solar surface flows. Astron. Astrophys. 512:A4 [Google Scholar]
  102. Rogers TM, Glatzmaier GA. 2005. Penetrative convection within the anelastic approximation. Astrophys. J. 620:432–41 [Google Scholar]
  103. Rüdiger G, Küker M, Tereshin I. 2014. The existence of the Λ effect in the solar convection zone as indicated by SDO/HMI data. Astron. Astrophys. 572:L7 [Google Scholar]
  104. Schou J. 2003. Wavelike properties of solar supergranulation detected in Doppler shift data. Astrophys. J. 596:L259–62 [Google Scholar]
  105. 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 [Google Scholar]
  106. Schou J, Scherrer PH, Bush RI, Wachter R, Couvidat S. et al. 2012. Design and ground calibration of the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). Sol. Phys. 275:229–59Describes the purpose and workings of the HMI onboard the Solar Dynamics Observatory, launched by NASA in 2010. [Google Scholar]
  107. Schrijver CJ, Hagenaar HJ, Title AM. 1997. On the patterns of the solar granulation and supergranulation. Astrophys. J. 475:328–37 [Google Scholar]
  108. Sekii T, Kosovichev AG, Zhao J, Tsuneta S, Shibahashi H. et al. 2007. Initial helioseismic observations by Hinode/SOT. Publ. Astron. Soc. 59:S637–41 [Google Scholar]
  109. Shishkina O, Horn S, Wagner S, Ching ESC. 2015. Thermal boundary layer equation for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 114:114302 [Google Scholar]
  110. Siggia E. 1994. High Rayleigh number convection. Annu. Rev. Fluid Mech. 26:137–68 [Google Scholar]
  111. Spiegel EA, Zahn JP. 1992. The solar tachocline. Astron. Astrophys. 265:106–14 [Google Scholar]
  112. Spruit HC. 1974. A model of the solar convection zone. Sol. Phys. 34:277–90 [Google Scholar]
  113. Spruit HC. 1997. Convection in stellar envelopes: a changing paradigm. Mem. Soc. Astron. Ital. 68:397–413 [Google Scholar]
  114. Stein RF, Nordlund Å. 2000. Realistic solar convection simulations. Sol. Phys. 192:91–108 [Google Scholar]
  115. Stevens R, Clercx H, Lohse D. 2010. Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection. New J. Phys. 12:075005 [Google Scholar]
  116. Stevens R, Clercx H, Lohse D. 2013. Heat transport and flow structure in rotating Rayleigh–Bénard convection. Eur. J. Mech. B/Fluids 40:41–49 [Google Scholar]
  117. Švanda M. 2012. Inversions for average supergranular flows using finite-frequency kernels. Astrophys. J. Lett. 759:L29 [Google Scholar]
  118. Švanda M, Gizon L, Hanasoge SM, Ustyugov SD. 2011. Validated helioseismic inversions for 3D vector flows. Astron. Astrophys. 530:A148 [Google Scholar]
  119. Urban P, Hanzelka P, Musilová V, Králk T, La Mantia M. et al. 2014. Heat transfer in cryogenic helium gas by turbulent Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1. New J. Phys. 16:053042 [Google Scholar]
  120. Vögler A, Shelyag S, Schüssler M, Cattaneo F, Emonet T, Linde T. 2005. Simulations of magneto-convection in the solar photosphere: equations, methods, and results of the MURaM code. Astron. Astrophys. 429:335–51 [Google Scholar]
  121. Weiss A, Hillebrandt W, Thomas H, Ritter H. 2004. Cox and Giuli's Principles of Stellar Structure Cambridge, UK: Cambridge Sci.
  122. Woodard MF. 2007. Probing supergranular flow in the solar interior. Astrophys. J. 668:1189–95 [Google Scholar]
  123. Woodward RL, Masters G. 1991. Lower-mantle structure from ScS–S differential travel times. Nature 352:231–33 [Google Scholar]
  124. Zahn JP. 1991. Convective penetration in stellar interiors. Astron. Astrophys. 252:179–88 [Google Scholar]
/content/journals/10.1146/annurev-fluid-122414-034534
Loading
Seismic Sounding of Convection in the Sun
Annual Review of Fluid Mechanics 48, 191 (2016); https://doi.org/10.1146/annurev-fluid-122414-034534
/content/journals/10.1146/annurev-fluid-122414-034534
/content/journals/10.1146/annurev-fluid-122414-034534
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error