Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers

Physics of Fluids

Volumn 21, Issue 1, 2009, Pages

  Mininni, P D ^a,b   Alexakis, A ^c   Pouquet, A ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^c UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY TRANSFER; REYNOLDS NUMBER;

ASTROPHYSICAL FLOWS; AXIS OF ROTATION; DIRECT TRANSFER; ENERGY INJECTION; ENERGY-CONTAINING EDDIES; SCALE INTERACTIONS; SPECTRAL BEHAVIORS; SPECTRAL SPACES;

ROTATION;

EID: 59649105993     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3064122     Document Type: Article

References (61)

1. J. Pedlosky, Geophysical Fluid Dynamics (Springer, Berlin, 1986).
2. M. S. Miesch, J. R. Elliott, J. T. T. L. Clune, G. A. Glatzmaier, and P. A. Gilman, "Three-dimensional spherical simulations of solar convection. I. Differential rotation and pattern evolution achieved with laminar and turbulent states," Astrophys. J. ASJOAB0004-637X 532, 593 (2000).
3. H. P. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, Cambridge, 1968).
4. F. Waleffe, "Inertial transfers in the helical decomposition," Phys. Fluids A PFADEB0899-821310.1063/1.858651 5, 677 (1993).
5. C. Cambon and L. Jacquin, "Spectral approach to non-isotropic turbulence subjected to rotation," J. Fluid Mech. JFLSA70022-112010.1017/S0022112089001199 202, 295 (1989).
6. C. Cambon, N. N. Mansour, and F. S. Godeferd, "Energy transfer in rotating turbulence," J. Fluid Mech. JFLSA70022-112010.1017/ S002211209700493X 337, 303 (1997).
7. S. Galtier, "Weak inertial-wave turbulence theory," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.68.015301 68, 015301 (2003).
8. P. F. Embid and A. Majda, "Averaging over fast gravity waves for geophysics flows with arbitrary potential vorticity," Commun. Partial Differ. Equ. CPDIDZ0360-530210.1080/03605309608821200 21, 619 (1996).
9. A. Babin, A. Mahalov, and B. Nicolaenko, "Global splitting, integrability and regularity of three-dimensional Euler and Navier-Stokes equations for uniformly rotating fluids," Eur. J. Mech. B/Fluids EJBFEV0997-7546 15, 291 (1996).
10. F. Bellet, F. S. Godeferd, J. F. Scott, and C. Cambon, "Wave turbulence in rapidly rotating flows," J. Fluid Mech. JFLSA70022-112010.1017/S0022112006000929 562, 83 (2006).
11. L. M. Smith and Y. Lee, "On near resonances and symmetry breaking in forced rotating flows at moderate rossby number," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005004660 535, 111 (2005).
12. P. J. Staplehurst, P. A. Davidson, and S. B. Dalziel, "Structure formation in homogeneous freely decaying rotating turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112007000067 598, 81 (2008).
13. L. J. A. van Bokhoven, C. Cambon, L. Liechtenstein, F. S. Godeferd, and H. J. H. Clercx, "Refined vorticity statistics of decaying rotating three-dimensional turbulence," J. Turbul. ZZZZZZ1468-5248 9, N6 (2008).
14. O. Zeman, "A note on the spectra and decay of rotating homogeneous turbulence," Phys. Fluids PHFLE61070-663110.1063/1.868053 6, 3221 (1994).
15. Y. Zhou, "A phenomenological treatment of rotating turbulence," Phys. Fluids PHFLE61070-663110.1063/1.868457 7, 2092 (1995).
16. V. M. Canuto and M. S. Dubovikov, "A dynamical model for turbulence. V. The effect of rotation," Phys. Fluids PHFLE61070-663110.1063/1.869332 9, 2132 (1997).
17. W.-C. Müller and M. Thiele, "Scaling and energy transfer in rotating turbulence," Europhys. Lett. EULEEJ0295-507510.1209/ 0295-5075/77/34003 77, 34003 (2007).
18. J. Bardina, J. H. Ferziger, and R. S. Rogallo, "Effect of rotation on isotropic turbulence: Computation and modeling," J. Fluid Mech. JFLSA70022-112010.1017/S0022112085001550 154, 321 (1985).
19. M. Hossain, "Reduction in the dimensionality of turbulence due to a strong rotation," Phys. Fluids PHFLE61070-663110.1063/1.868278 6, 1077 (1994).
20. P. Bartello, O. Métais, and M. Lesieur, "Coherent structures in rotating three-dimensional turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112094001837 273, 1 (1994).
21. L. M. Smith, J. R. Chasnov, and F. Waleffe, "Crossover from two-to three-dimensional turbulence," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.77.2467 77, 2467 (1996).
22. L. M. Smith and F. Waleffe, "Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence," Phys. Fluids PHFLE61070-663110.1063/1.870022 11, 1608 (1999).
23. P. K. Yeung and Y. Zhou, "Numerical study of rotating turbulence with external forcing," Phys. Fluids PHFLE61070-663110.1063/ 1.869810 10, 2895 (1998).
24. Q. Chen, S. Chen, G. L. Eyink, and D. Holm, "Resonant interactions in rotating homogeneous three-dimensional turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005006324 542, 139 (2005).
25. P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics (Cambridge University Press, Cambridge, 2008).
26. G. I. Taylor and A. E. Green, "Mechanism of the production of small eddies from large ones," Proc. R. Soc. London, Ser. A PRLAAZ0950-120710.1098/rspa.1937.0036 158, 499 (1937).
27. R. H. Morf, S. A. Orszag, and U. Frisch, "Spontaneous singularity in three-dimensional, inviscid, incompressible flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.44.572 44, 572 (1980).
28. C. Simand, F. Chillà, and J.-F. Pinton, "Study of inhomogeneous turbulence in the closed flow between corotating disks," Europhys. Lett. EULEEJ0295-507510.1209/epl/i2000-00501-8 49, 336 (2000).
29. R. Monchaux, M. Berhanu, M. Bourgoin, M. Moulin, Ph. Odier, J.-F. Pinton, R. Volk, S. Fauve, N. Mordant, F. Pétrélis, A. Chiffaudel, F. Daviaud, B. Dubrulle, C. Gasquet, L. Marié, and F. Ravelet, "Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.98.044502 98, 044502 (2007).
30. A. Alexakis, P. D. Mininni, and A. Pouquet, "Shell-to-shell energy transfer in magnetohydrodynamics. I. steady state turbulence," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.72.046301 72, 046301 (2005).
31. P. D. Mininni, A. Alexakis, and A. Pouquet, "Shell-to-shell energy transfer in magnetohydrodynamics. II. kinematic dynamo," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.72.046302 72, 046302 (2005).
32. A. Alexakis, P. D. Mininni, and A. Pouquet, "Imprint of large-scale flows on turbulence," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.95.264503 95, 264503 (2005).
33. P. D. Mininni, A. Alexakis, and A. Pouquet, "Large-scale flow effects, energy transfer, and self-similarity on turbulence," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.74.016303 74, 016303 (2006).
34. A. Alexakis, B. Bigot, H. Politano, and S. Galtier, "Anisotropic fluxes and nonlocal interactions in magnetohydrodynamic turbulence," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.76.056313 76, 056313 (2007).
35. J. A. Domaradzki, "Analysis of energy transfer in direct numerical simulations of isotropic turbulence," Phys. Fluids PFLDAS0031-917110.1063/1.866980 31, 2747 (1988).
36. J. A. Domaradzki and R. S. Rogallo, "Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence," Phys. Fluids A PFADEB0899-821310.1063/1.857736 2, 413 (1990).
37. P. D. Mininni, A. Alexakis, and A. Pouquet, "Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws," Phys. Rev. E PLEEE81063-651X10.1103/ PhysRevE.77.036306 77, 036306 (2008).
38. A. Alexakis, P. D. Mininni, and A. Pouquet, "On the inverse cascade of magnetic helicity," Astrophys. J. ASJOAB0004-637X10.1086/500082 640, 335 (2006).
39. A. Alexakis, P. D. Mininni, and A. Pouquet, "Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics," New J. Phys. NJOPFM1367-263010.1088/1367-2630/9/8/298 9, 298 (2007).
40. J. C. McWilliams, "The emergence of isolated coherent vortices in turbulent flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112084001750 146, 21 (1984).
41. M. E. Brachet, M. Meneguzzi, and P. L. Sulem, "Small-scale dynamics of high-Reynolds-number two-dimensional turbulence," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.57.683 57, 683 (1986).
42. A. Babiano, C. Basdevant, B. Legras, and R. Sadourny, "Vorticity and passive-scalar dynamics in two-dimensional turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112087002684 183, 379 (1987).
43. R. Benzi, S. Patarnello, and P. Santangelo, "On the statistical properties of two-dimensional decaying turbulence," Europhys. Lett. EULEEJ0295-507510.1209/0295-5075/3/7/007 3, 811 (1987).
44. M. E. Maltrud and G. K. Vallis, "Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence," J. Fluid Mech. JFLSA70022-1120 228, 321 (1991).
45. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
46. P. D. Mininni and A. Pouquet, "Energy spectra stemming from interactions of Alfvén waves and turbulent eddies," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.99.254502 99, 254502 (2007).
47. P. S. Iroshnikov, "Turbulence of a conducting fluid in a strong magnetic field," Sov. Astron. SAAJAN0038-5301 7, 566 (1963).
48. R. H. Kraichnan, "Inertial-range spectrum of hydromagnetic turbulence," Phys. Fluids PFLDAS0031-917110.1063/1.1761412the 8, 1385 (1965).
49. Z. S. She and E. Lévêque, "Universal scaling laws in fully developed turbulence," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.72.336 72, 336 (1994).
50. L. Jacquin, O. Leuchter, C. Cambon, and J. Mathieu, "Homogeneous turbulence in the presence of rotation," J. Fluid Mech. JFLSA70022-112010.1017/S0022112090003172 220, 1 (1990).
51. J. V. Shebalin, W. H. Matthaeus, and D. Montgomery, "Anisotropy in MHD turbulence due to a mean magnetic field," J. Plasma Phys. JPLPBZ0022-3778 29, 525 (1983).
52. L. J. Milano, W. H. Matthaeus, P. Dmitruk, and D. C. Montgomery, "Local anisotropy in incompressible magnetohydrodynamic turbulence," Phys. Plasmas PHPAEN1070-664X10.1063/1.1369658 8, 2673 (2001).
53. L. Liechtenstein, F. S. Godeferd, and C. Cambon, "Nonlinear formation of structures in rotating stratified turbulence," J. Turbul. ZZZZZZ1468-5248 6, 1 (2005).
54. Y. Morinishi, K. Nakabayashi, and S. Ren, "Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation," Phys. Fluids PHFLE61070-663110.1063/1.1398040 13, 2912 (2001).
55. X. Yang and J. A. Domaradzki, "LES of decaying rotating turbulence," Phys. Fluids PHFLE61070-663110.1063/1.1790452 16, 4088 (2004).
56. R. Benzi and R. Scardovelli, "Intermittency of two-dimensional decaying turbulence," Europhys. Lett. EULEEJ0295-507510.1209/ 0295-5075/29/5/004 29, 371 (1995).
57. G. Boffetta, "Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence," J. Fluid Mech. JFLSA70022-1120 589, 253 (2007).
58. P. Charbonneau, "Multiperiodicity, chaos, and intermittency in a reduced model of the solar cycle," Sol. Phys. SLPHAX0038-093810.1023/A:1010387509792 199, 385 (2001).
59. P. D. Mininni, D. O. Gómez, and G. B. Mindlin, "Biorthogonal decomposition techniques unveil the nature of the irregularities observed in the solar cycle," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.89.061101 89, 061101 (2002).
60. J. R. Kulkarni, L. K. Sadani, and B. S. Murthy, "Wavelet analysis of intermittent turbulent transport in the atmospheric surface layer over a monsoon trough region," Boundary-Layer Meteorol. BLMEBR0006-831410.1023/A:1001773312285 90, 217 (1999).
61. J. Clyne, P. Mininni, A. Norton, and M. Rast, "Interactive desktop analysis of high resolution simulations: Application to turbulent plume dynamics and current sheet formation," New J. Phys. NJOPFM1367-263010.1088/1367-2630/9/8/301 9, 301 (2007).