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Forcing-dependent dynamics and emergence of helicity in rotating turbulence

Published online by Cambridge University Press:  08 June 2016

Vassilios Dallas  and
Steven M. Tobias
Vassilios Dallas*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Steven M. Tobias
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: v.dallas@leeds.ac.uk
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Abstract

The effects of large-scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of direct numerical simulations, systematically varying the nature of the mechanical force in time. We find that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relative to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We demonstrate that the nature of the mechanical force in time and the emergence of helicity have direct implications for the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak turbulence.

JFM classification

Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 682 - 695
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Copyright
© 2016 Cambridge University Press 

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References

Alexakis, A. 2015 Rotating Taylor–Green flow. J. Fluid Mech. 769, 46–78.CrossRefGoogle Scholar
André, J. C. & Lesieur, M. 1977 Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187–207.CrossRefGoogle Scholar
Bartello, P., Métais, O. & Lesieur, M. 1994 Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech. 273, 1–29.Google Scholar
Bewley, G. P., Lathrop, D. P., Maas, L. R. M. & Sreenivasan, K. R. 2007 Inertial waves in rotating grid turbulence. Phys. Fluids 19, 071701.Google Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44 (1), 427–451.CrossRefGoogle Scholar
van Bokhoven, L. J. A., Clercx, H. J. H., van Heijst, G. J. F. & Trieling, R. R. 2009 Experiments on rapidly rotating turbulent flows. Phys. Fluids 21, 096601.Google Scholar
Bracco, A. & McWilliams, J. C. 2010 Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence. J. Fluid Mech. 646, 517–526.Google Scholar
Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332.CrossRefGoogle Scholar
Constantin, P. & Majda, A. 1988 The Beltrami spectrum for incompressible fluid flows. Commun. Math. Phys. 115, 435–456.Google Scholar
Dallas, V. & Alexakis, A. 2015 Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows. Phys. Fluids 27, 045105.Google Scholar
Dallas, V., Fauve, S. & Alexakis, A. 2015 Statistical equilibria of large scales in dissipative hydrodynamic turbulence. Phys. Rev. Lett. 115, 204501.CrossRefGoogle ScholarPubMed
Davidson, P. A., Staplehurst, P. J. & Dalziel, S. B. 2006 On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144.CrossRefGoogle Scholar
Deusebio, E., Boffetta, G., Lindborg, E. & Musacchio, S. 2014 Dimensional transition in rotating turbulence. Phys. Rev. E 90, 023005.Google Scholar
Dombre, T., Frisch, U., Greene, J. M., Hnon, M., Mehr, A. & Soward, A. M. 1986 Chaotic streamlines in the abc flows. J. Fluid Mech. 167, 353–391.Google Scholar
Galtier, S. 2003 Weak inertial-wave turbulence theory. Phys. Rev. E 68, 015301.Google ScholarPubMed
Gómez, D. O., Mininni, P. D. & Dmitruk, P. 2005 Parallel simulations in turbulent MHD. Phys. Scr. T116, 123–127.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Hide, R. 1975 A note on helicity. Geophys. Fluid Dyn. 7 (1), 157–161.CrossRefGoogle Scholar
Hopfinger, E. J. & Heijst, G. J. F. V. 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241–289.Google Scholar
Hossain, M. 1994 Reduction in the dimensionality of turbulence due to a strong rotation. Phys. Fluids 6, 1077–1080.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Lighthill, J. 1965 Waves in Fluids. Cambridge University Press.Google Scholar
Maltrud, M. E. & Vallis, G. K. 1991 Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech. 228, 321–342.Google Scholar
Marino, R., Mininni, P. D., Rosenberg, D. & Pouquet, A. 2013 Emergence of helicity in rotating stratified turbulence. Phys. Rev. E 87, 033016.Google Scholar
Markowski, P. M., Straka, J. M., Rasmussen, E. N. & Blanchard, D. O. 1998 Variability of storm-relative helicity during VORTEX. Mon. Weath. Rev. 126 (11), 2959–2971.Google Scholar
Mininni, P. D., Alexakis, A. & Pouquet, A. 2009 Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers. Phys. Fluids 21, 015108.Google Scholar
Mininni, P. D. & Pouquet, A. 2009 Helicity cascades in rotating turbulence. Phys. Rev. E 79, 026304.Google ScholarPubMed
Mininni, P. D. & Pouquet, A. 2010 Rotating helical turbulence. I: global evolution and spectral behavior. Phys. Fluids 22, 035105.Google Scholar
Mininni, P. D., Rosenberg, D. & Pouquet, A. 2012 Isotropization at small scales of rotating helically driven turbulence. J. Fluid Mech. 699, 263–279.Google Scholar
Moffatt, H. K. 1970 Dynamo action associated with random inertial waves in a rotating conducting fluid. J. Fluid Mech. 44, 705–719.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Moisy, F., Morize, C., Rabaud, M. & Sommeria, J. 2011 Decay laws, anisotropy and cyclone – anticyclone asymmetry in decaying rotating turbulence. J. Fluid Mech. 666, 5–35.CrossRefGoogle Scholar
Morinishi, Y., Nakabayashi, K. & Ren, S. 2001 Effects of helicity and system rotation on decaying homogeneous turbulence. JSME Intl J. B 44, 410–418.CrossRefGoogle Scholar
Pouquet, A. & Mininni, P. D. 2010 The interplay between helicity and rotation in turbulence: implications for scaling laws and small-scale dynamics. Phil. Trans. R. Soc. Lond. A 368 (1916), 1635–1662.Google ScholarPubMed
Pouquet, A., Sen, A., Rosenberg, D., Mininni, P. D. & Baerenzung, J. 2013 Inverse cascades in turbulence and the case of rotating flows. Phys. Scr. T 155, 014032.Google Scholar
Proudman, J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. R. Soc. Lond. A 92 (642), 408–424.Google Scholar
Ruppert-Felsot, J. E., Praud, O., Sharon, E. & Swinney, H. L. 2005 Extraction of coherent structures in a rotating turbulent flow experiment. Phys. Rev. E 72, 016311.Google Scholar
Sen, A., Mininni, P. D., Rosenberg, D. & Pouquet, A. 2012 Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence. Phys. Rev. E 86, 036319.Google Scholar
Smith, L. M., Chasnov, J. R. & Waleffe, F. 1996 Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 77, 2467–2470.CrossRefGoogle ScholarPubMed
Taylor, G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. R. Soc. Lond. A 93 (648), 99–113.Google Scholar
Teitelbaum, T. & Mininni, P. D. 2011 The decay of turbulence in rotating flows. Phys. Fluids 23 (6), 065105.CrossRefGoogle Scholar
Tobias, S. M. 2009 The solar dynamo: the role of penetration, rotation and shear on convective dynamos. Space Sci. Rev. 144, 77–86.CrossRefGoogle Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics. Clarendon Press.Google Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4 (2), 350–363.Google Scholar
Yeung, P. K. & Zhou, Y. 1998 Numerical study of rotating turbulence with external forcing. Phys. Fluids 10, 2895–2909.Google Scholar
Yoshimatsu, K., Midorikawa, M. & Kaneda, Y. 2011 Columnar eddy formation in freely decaying homogeneous rotating turbulence. J. Fluid Mech. 677, 154–178.Google Scholar
Zhou, Y. 1995 A phenomenological treatment of rotating turbulence. Phys. Fluids 7 (8), 2092–2094.Google Scholar