Abstract
In a density-stratified turbulent medium, the cross helicity 〈u′⋅B′〉 is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s−1. Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.
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References
Bochner, S.: 1933, Math. Ann. 108, 378.
Brandenburg, A., Dobler, W.: 2002, Comput. Phys. Commun. 147, 471.
Brandenburg, A., Subramanian, K.: 2005, Phys. Rep. 417, 1.
Duvall, T.L. Jr., Gizon, L.: 2000, Solar Phys. 192, 177.
Egorov, P., Rüdiger, G., Ziegler, U.: 2004, Astron. Astrophys. 425, 725.
Käpylä, P.J., Korpi, M.J., Brandenburg, A.: 2009, Astron. Astrophys. 500, 633.
Keinigs, R.K.: 1983, Phys. Fluids 26, 2558.
Kitchatinov, L.L.: 1991, Astron. Astrophys. 243, 483.
Kleeorin, N., Kuzanyan, K., Moss, D., Rogachevskii, I., Sokoloff, D., Zhang, H.: 2003, Astron. Astrophys. 409, 1097.
Kolmogorov, A.N.: 1941, Dokl. Akad. Nauk USSR 32, 16.
Komm, R., Hill, F., Howe, R.: 2008, J. Phys. Conf. Ser. 118, 012035.
Krause, F., Rüdiger, G.: 1975, Solar Phys. 42, 107.
Krivodubskij, V.N., Schultz, M.: 1992, In: Krause, F., Rädler, K.-H., Rüdiger, G. (eds.) The Cosmic Dynamo, IAU Symp. 157, 25.
Kuzanyan, K.M., Pipin, V.V., Zhang, H.: 2007, Adv. Space Res. 39, 1649.
Moffatt, H.K.: 1969, J. Fluid Mech. 35, 117.
Rüdiger, G., Hollerbach, R.: 2004, The Magnetic Universe: Geophysical and Astrophysical Dynamo Theory, Wiley-VCH, Berlin, 81.
Rüdiger, G., Brandenburg, A., Pipin, V.V.: 1999, Astron. Nachr. 320, 135.
Schrijver, C.J., Martin, S.F.: 1990, Solar Phys. 129, 95.
Seehafer, N.: 1990, Solar Phys. 125, 219.
Sur, S., Brandenburg, A., Subramanian, K.: 2008, Mon. Not. Roy. Astron. Soc. 385, L15.
Sur, S., Brandenburg, A.: 2009, Mon. Not. Roy. Astron. Soc. 399, 273.
Stix, M.: 1989, The Sun: An Introduction, Springer, Berlin, 287.
Woltjer, L.: 1958, Proc. Natl. Acad. Sci. 44, 833.
Yokoi, N.: 1996, Astron. Astrophys. 311, 731.
Yoshizawa, A.: 1990, Phys. Fluids B 2, 1589.
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Rüdiger, G., Kitchatinov, L.L. & Brandenburg, A. Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone. Sol Phys 269, 3–12 (2011). https://doi.org/10.1007/s11207-010-9683-4
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DOI: https://doi.org/10.1007/s11207-010-9683-4