Abstract
This study investigates the combined effect of density, velocity and magnetic field gradients on the Kelvin–Helmholtz instability of two viscous fluid layers. For the linear phase of instability that refers to the early stage of development of Kelvin–Helmholtz instability, the linear growth rate and frequency are presented. With respect to our selected variables and the Atwood number, the behaviour of growth rate and frequency are analysed. It is found that, the behaviour of frequency is not affected by the magnetic field and viscous term. The velocity gradient with the small Atwood numbers tends to stabilize KHI flows, while the velocity gradient with the large Atwood numbers has destabilizing effect on KHI. The growth rate reduces with the constant magnetic field and viscous term, while it enhances with magnetic field gradient.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amerstorfer, U.V., Erkaev, N.V., Langmayr, D., Biernat, H.K.: Planet. Space Sci. 55, 1811 (2007)
Bettarini, L., Landi, S., Rappazzo, F.A., Velli, M., Opher, M.: Astron. Astrophys. 452, 321 (2006)
Cavus, H., Kazkapan, D.: New Astron. 25, 89 (2013)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Dower Publications Inc., New York (19610)
Foullon, C., Verwichte, E., Nakariakov, V.M., Nykyri, K., Farrugia, C.J.: Astrophys. J. Lett. 729, 1 (2011)
Gogoberidze, G., Voitenko, Y.M.: Astrophys. Space Sci. 364, 361 (2016)
Hasegawa, H., Fujimoto, M., Phan, T.D., Reme, H., Balogh, A., Dunlop, M.W.: Nature 415, 755 (2004)
Helmholtz, H.L.F.: Sitz.ber. Preuss. Akad. Wiss. Berl. Philos.-Hist. Kl. 23, 215 (1868)
Hoshoudy, G.A.: Arab. J. Sci. Eng. 36, 105 (2011)
Hoshoudy, G.A., Cavus, H.: J. Astrophys. Astron. 39, 39 (2018)
Kelvin, L.W.T.: Philos. Mag. 42, 362 (1871)
Kimura, H., Mann, I.: Earth Planets Space 50, 493 (1998)
Kimura, H., Mann, I., Mukai, T.: Planet. Space Sci. 8, 911 (1998)
Knoll, D.A., Brackbill, J.U.: Phys. Plasmas 9, 3775 (2002)
Krivov, A., Kimura, H., Mann, I.: Icarus 134, 311 (1998)
Kuridze, D., Henriques, V., Mathioudakis, M., Erdélyi, R., Zaqarashvili, T.V., Shelyag, S., Keys, P.H., Keenan, F.P.: Astrophys. J. 802, 26 (2015)
Kuridze, D., Zaqarashvili, T.V., Henriques, V., Mathioudakis, M., Keenan, F.P., Hanslmeier, A.: Astrophys. J. 830, 133 (2016)
Landi, S., Velli, M.: Mem. Soc. Astron. Ital. 13, 39 (2009)
Lapenta, G., Knoll, D.A.: Sol. Phys. 214, 107 (2003)
Li, L.X., Narayan, R.: Astrophys. J. 601, 414 (2004)
Li, W., André, M., Khotyaintsev, Y.V., Vaivads, A., Graham, D.B., et al.: Geophys. Res. Lett. 43, 5635 (2016)
Mann, I., Okamoto, H., Mukai, T., Kimura, H., Kitada, Y.: Astron. Astrophys. 291, 1011 (1994)
Mann, I., Krivov, A., Kimura, H.: Icarus 146, 568 (2000)
Mishin, V.V., Tomozov, V.M.: Sol. Phys. 291, 3165 (2016)
Nakamura, T.K.M., Fujimoto, M., Otto, A.: Geophys. Res. Lett. 33, L14106 (2006)
Ofman, L., Thompson, B.J.: Astrophys. J. Lett. 734, 1 (2011)
Squire, H.B.: Proc. R. Soc. Lond., a Contain. Pap. Math. Phys. Character 142, 621 (1933)
Velli, M., Einaudi, G., Chiuderi, C., Veltri, P.L.: Mem. Soc. Astron. Ital. 74, 425 (2003)
Wang, L.F., Xue, C., Ye, W.H., Li, Y.J.: Phys. Plasmas 16, 112104 (2009)
Wang, L.F., Ye, W.H., Li, Y.J.: Phys. Plasmas 17, 042103 (2010)
Yang, B.L., Wang, L.F., Ye, W.H., Xue, C.: Phys. Plasmas 18, 072111 (2011)
Ye, W.H., Wang, L.F., Xue, C., Fan, Z.F., He, X.T.: Phys. Plasmas 18, 022704 (2011)
Yong, J.C., Oh, S.H., Min, K.: Astrophys. Space Sci. 236, 201 (1996)
Zhao, K.G., Wang, L.F., Ye, W.H., Wu, J.F., Li, Y.J.: Chin. Phys. Lett. 31, 030401 (2014)
Zhelyazkov, I., Chandra, R., Srivastava, A.K., Mishonov, T.: Astrophys. Space Sci. 356, 231 (2015)
Acknowledgements
The authors would like to thank the referees for their interest in this work and for their many constructive suggestions that improved the original manuscript. We would like also to thank Dr. M. Elsayed (Department of Mathematics and Computer Science, Faculty of Science, South Valley University, Qena, Egypt) for assisting in the revising process.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hoshoudy, G.A., Cavus, H. & Mahdy, A. A viscous magnetohydrodynamic Kelvin–Helmholtz instability in the interface of two fluid layers: Part I. Basic mechanism. Astrophys Space Sci 364, 89 (2019). https://doi.org/10.1007/s10509-019-3576-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-019-3576-2