Skip to main content Accessibility help

Small-scale dynamo action in rotating compressible convection

  • B. Favier (a1) and P. J. Bushby (a1)


We study dynamo action in a convective layer of electrically conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number that is based upon the horizontal integral scale and the horizontally averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9 % of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.


Corresponding author

Email address for correspondence:


Hide All
1. Baliunas, S. L., Nesme-Ribes, E., Sokoloff, D. & Soon, W. H. 1996 A dynamo interpretation of stellar activity cycles. Astrophys. J. 460, 848854.
2. Brandenburg, A., Jennings, R. L., Nordlund, Å., Rieutord, M., Stein, R. F. & Tuominen, I. 1996 Magnetic structures in a dynamo simulation. J. Fluid Mech. 306, 325352.
3. Brandenburg, A., Klapper, I. & Kurths, J. 1995 Generalized entropies in a turbulent dynamo simulation. Phys. Rev. E 52, R4602R4605.
4. Brummell, N. H., Cattaneo, F. & Tobias, S. M. 1998a Linear and nonlinear dynamo action. Phys. Lett. A 249, 437442.
5. Brummell, N. H., Hurlburt, N. E. & Toomre, J. 1996 Turbulent compressible convection with rotation. Part I. Flow structure and evolution. Astrophys. J. 473, 494513.
6. Brummell, N. H., Hurlburt, N. E. & Toomre, J. 1998b Turbulent compressible convection with rotation. Part II. Mean flows and differential rotation. Astrophys. J. 493, 955969.
7. Brummell, N. H., Tobias, S. M. & Cattaneo, F. 2010 Dynamo efficiency in compressible convective dynamos with and without penetration. Geophys. Astrophys. Fluid Dyn. 104, 565576.
8. Brun, A. S., Miesch, M. S. & Toomre, J. 2004 Global-scale turbulent convection and magnetic dynamo action in the solar envelope. Astrophys. J. 614, 10731098.
9. Bushby, P. J., Houghton, S. M., Proctor, M. R. E. & Weiss, N. O. 2008 Convective intensification of magnetic fields in the quiet sun. Mon. Not. R. Astron. Soc. 387, 698706.
10. Bushby, P. J., Proctor, M. R. E. & Weiss, N. O. 2010 Small-scale dynamo action in compressible convection. In Numerical Modelling of Space Plasma Flows, Astronum-2009 (ed. Pogorelov, N. V., Audit, E. & Zank, G. P. ). Astronomical Society of the Pacific Conference Series , vol. 429, pp. 181186.
11. Cattaneo, F. 1999 On the origin of magnetic fields in the quiet photosphere. Astrophys. J. 515, L39L42.
12. Cattaneo, F. & Hughes, D. W. 2006 Dynamo action in a rotating convective layer. J. Fluid Mech. 553, 401418.
13. Cattaneo, F., Hughes, D. W. & Kim, E. 1996 Suppression of chaos in a simplified nonlinear dynamo model. Phys. Rev. Lett. 76, 20572060.
14. Cattaneo, F. & Tobias, S. M. 2009 Dynamo properties of the turbulent velocity field of a saturated dynamo. J. Fluid Mech. 621, 205214.
15. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
16. Childress, S. & Soward, A. M. 1972 Convection-driven hydromagnetic dynamo. Phys. Rev. Lett. 29, 837839.
17. Eckhardt, B. & Yao, D. 1993 Local Lyapunov exponents in chaotic systems. Physica D 65, 100108.
18. Favier, B. F. N., Godeferd, F. S. & Cambon, C. 2011 On the effect of rotation on MHD turbulence at high magnetic Reynolds number. Geophys. Astrophys. Fluid Dyn.
19. Finn, J. M. & Ott, E. 1988 Chaotic flows and fast magnetic dynamos. Phys. Fluids 31, 29923011.
20. Gough, D. O., Moore, D. R., Spiegel, E. A. & Weiss, N. O. 1976 Convective instability in a compressible atmosphere. Part II. Astrophys. J. 206, 536542.
21. Haugen, N. E. L., Brandenburg, A. & Dobler, W. 2004 Simulations of nonhelical hydromagnetic turbulence. Phys. Rev. E 70, 016308.
22. Hughes, D. W. & Proctor, M. R. E. 2009 Large-scale dynamo action driven by velocity shear and rotating convection. Phys. Rev. Lett. 102, 044501.
23. Jones, C. A. & Roberts, P. H. 2000 Convection-driven dynamos in a rotating plane layer. J. Fluid Mech. 404, 311343.
24. Käpylä, P. J., Korpi, M. J. & Brandenburg, A. 2008 Large-scale dynamos in turbulent convection with shear. Astron. Astrophys. 491, 353362.
25. Käpylä, P. J., Korpi, M. J. & Brandenburg, A. 2009 Large-scale dynamos in rigidly rotating turbulent convection. Astrophys. J. 697, 11531163.
26. Käpylä, P. J., Korpi, M. J. & Brandenburg, A. 2010 Open vs closed boundaries in large-scale convective dynamos. Astron. Astrophys. 518, A22.
27. Matthews, P. C., Proctor, M. R. E. & Weiss, N. O. 1995 Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour. J. Fluid Mech. 305, 281305.
28. Meneguzzi, M. & Pouquet, A. 1989 Turbulent dynamos driven by convection. J. Fluid Mech. 205, 297398.
29. Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
30. Monchaux, R., Berhanu, M., Aumaître, S., Chiffaudel, A., Daviaud, F., Dubrulle, B., Ravelet, F., Fauve, S., Mordant, N., Pétrélis, F., Bourgoin, M., Odier, P., Pinton, J.-F., Plihon, N. & Volk, R. 2009 The von Kármán sodium experiment: turbulent dynamical dynamos. Phys. Fluids 21 (3), 035108.
31. Roberts, P. H. & Glatzmaier, G. A. 2000 Geodynamo theory and simulations. Rev. Mod. Phys. 72, 10811123.
32. Rogachevskii, I. & Kleeorin, N. 1997 Intermittency and anomalous scaling for magnetic fluctuations. Phys. Rev. E 56, 417426.
33. Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Maron, J. L. & McWilliams, J. C. 2004 Simulations of the small-scale turbulent dynamo. Astrophys. J. 612, 276307.
34. Servidio, S., Matthaeus, W. H. & Dmitruk, P. 2008 Depression of nonlinearity in decaying isotropic MHD turbulence. Phys. Rev. Lett. 100, 095005.
35. St. Pierre, M. G. 1993 The strong field branch of the Childress–Soward dynamo. In Solar and Planetary Dynamos (ed. Proctor, M. R. E., Matthews, P. C. & Rucklidge, A. M. ). pp. 295302.
36. Stellmach, S. & Hansen, U. 2004 Cartesian convection driven dynamos at low Ekman number. Phys. Rev. E 70, 056312.
37. Stix, M. 2004 The Sun: An Introduction. Springer.
38. Tanner, S. E. M. & Hughes, D. W. 2003 Fast-dynamo action for a family of parametrized flows. Astrophys. J. 586, 685691.
39. Thelen, J.-C. & Cattaneo, F. 2000 Dynamo action driven by convection: the influence of magnetic boundary conditions. Mon. Not. R. Astron. Soc. 315, L13L17.
40. Vögler, A. & Schüssler, M. 2007 A solar surface dynamo. Astron. Astrophys. 465, L43L46.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Small-scale dynamo action in rotating compressible convection

  • B. Favier (a1) and P. J. Bushby (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed