Solar Physics

, Volume 251, Issue 1–2, pp 469–489 | Cite as

Effects of Random Flows on the Solar f Mode: II. Horizontal and Vertical Flow

HELIOSEISMOLOGY, ASTEROSEISMOLOGY, AND MHD CONNECTIONS

Abstract

We study the influence of horizontal and vertical random flows on the solar f mode in a plane-parallel, incompressible model that includes a static atmosphere. The incompressible limit is an adequate approximation for f-mode type of surface waves that are highly incompressible. The paper revisits and extends the problem investigated earlier by Murawski and Roberts (Astron. Astrophys.272, 601, 1993).

We show that the consideration of the proposed velocity profile requires several restrictive assumptions to be made. These constraints were not recognised in previous studies. The impact of the inconsistencies in earlier modelling is analysed in detail. Corrections to the dispersion relation are derived and the relevance of these corrections is analysed. Finally, the importance of the obtained results is investigated in the context of recent helioseismological data. Detailed comparison with our complementary studies on random horizontal flows (Mole, Kerekes, and Erdélyi, Solar Phys., accepted, 2008) and the random magnetic model of Erdélyi, Kerekes, and Mole (Astron. Astrophys.431, 1083, 2005) is also given. In particular, for realistic solar parameters we find significant frequency reduction and wave damping, both of which increase with the characteristic thickness of the random layer.

Keywords

Surface gravity waves Turbulence Dispersion relation Damping 

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References

  1. Antia, H.M., Basu, S.: 1999, High-frequency and high-wavenumber solar oscillations. Astrophys. J. 519, 400 – 406. CrossRefADSGoogle Scholar
  2. Christensen-Dalsgaard, J.: 2002, Helioseismology. Rev. Mod. Phys. 74, 1073 – 1128. CrossRefADSGoogle Scholar
  3. Duvall, T.L., Kosovichev, A.G., Murawski, K.: 1998, Random damping and frequency reduction of the solar f-mode. Astrophys. J. 505, L55 – L58. CrossRefADSGoogle Scholar
  4. Erdélyi, R.: 2006, Magnetic coupling of waves and oscillations in the lower solar atmosphere: Can the tail wag the dog? Philos. Trans. Roy. Soc. A 364, 351 – 381. CrossRefADSGoogle Scholar
  5. Erdélyi, R., Kerekes, A., Mole, N.: 2005, Influence of random magnetic field on solar global oscillations: The incompressible f-mode. Astron. Astrophys. 431, 1083 – 1088. CrossRefADSGoogle Scholar
  6. Gruzinov, A.V.: 1998, Sound speed in a random flow and turbulent shifts of the solar eigenfrequencies. Astrophys. J. 498, 458 – 464. CrossRefADSGoogle Scholar
  7. Howe, M.S.: 1971, Wave propagation in random media. J. Fluid Mech. 45, 769 – 783. MATHCrossRefGoogle Scholar
  8. Kerekes, A.: 2007, Random effects on the solar f -mode. PhD thesis, University of Sheffield. Google Scholar
  9. Kerekes, A., Erdélyi, R., Mole, N.: 2008, A novel approach to the solar interior-atmosphere EVP. Astrophys. J., accepted. Google Scholar
  10. Krause, F., Roberts, P.H.: 1976, Some problems of mean field electrodynamics. Astrophys. J. 181, 977 – 992. CrossRefADSGoogle Scholar
  11. Mędrek, M., Murawski, K., Roberts, B.: 1999, Damping and frequency reduction of the f-mode due to turbulent motion in the solar convection zone. Astron. Astrophys. 349, 312 – 316. ADSGoogle Scholar
  12. Mole, N., Kerekes, A., Erdélyi, R.: 2008, Effect of random flows on the solar f-mode I.: Horizontal flow. Solar Phys., accepted. Google Scholar
  13. Murawski, K., Goossens, M.: 1993, Random velocity field corrections to the f-mode. III. A photospheric random flow and chromospheric magnetic field. Astron. Astrophys. 279, 225 – 234. ADSGoogle Scholar
  14. Murawski, K., Roberts, B.: 1993a, Random velocity field corrections to the f-mode. I. Horizontal flows. Astron. Astrophys. 272, 595 – 600. ADSGoogle Scholar
  15. Murawski, K., Roberts, B.: 1993b, Random velocity field corrections to the f-mode. II. Vertical and horizontal flow. Astron. Astrophys. 272, 601 – 608. ADSGoogle Scholar
  16. Rädler, K.H.: 1976, Mean-field magnetohydrodynamics as a basis of solar dynamo theory. In: Basic Mechanisms of Solar Activity, Proc. IAU Symposium 71, Reidel, Dordrecht, 323 – 344. Google Scholar
  17. Sazontov, A.G., Shagalov, S.V.: 1986, Scattering of gravity waves by a turbulence of the upper ocean layer. Izv. Atmos. Ocean. Phys. 22, 138 – 143. Google Scholar
  18. Selwa, M., Skartlien, R., Murawski, K.: 2004, Numerical simulations of stochastically excited sound waves in a random medium. Astron. Astrophys. 420, 1123 – 1127. CrossRefADSGoogle Scholar
  19. Skartlien, R.: 2002, Effects in the solar p-mode power spectrum from scattering on a turbulent background flow with stochastic wave sources. Astrophys. J. 578, 621 – 647. CrossRefADSGoogle Scholar
  20. Solanki, S.K., Inhester, B., Schüssler, M.: 2006, The solar magnetic field. Rep. Prog. Phys. 69, 563 – 668. CrossRefADSGoogle Scholar
  21. Spruit, H.C., Nordlund, A., Title, A.M.: 1990, Solar convection. Ann. Rev. Astron. Astrophys. 28, 263 – 301. CrossRefADSGoogle Scholar
  22. Stein, R.F., Nordlund, A.: 1998, Simulations of solar granulation. I. General properties. Astrophys. J. 499, 914 – 933. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Solar Physics and Space Plasma Research Centre, Department of Applied MathematicsUniversity of SheffieldSheffieldUK

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