Controlling the dual cascade of two-dimensional turbulence

Journal of Fluid Mechanics

Volumn 668, Issue , 2011, Pages 202-222

  Farazmand, M M ^a   Kevlahan, N K R ^b   Protas, B ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

turbulence control; turbulence simulation; turbulence theory

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL MODELS; REYNOLDS NUMBER; SPECTROSCOPY;

KOLMOGOROV THEORY; MODERATE REYNOLDS NUMBERS; THREE-DIMENSIONAL TURBULENCE; TIME-SPACE STRUCTURE; TURBULENCE CONTROLS; TURBULENCE SIMULATION; TURBULENCE THEORY; TWO DIMENSIONAL TURBULENCE;

TURBULENCE;

COMPUTER SIMULATION; FLOW CONTROL; NUMERICAL MODEL; REYNOLDS NUMBER; STATISTICAL ANALYSIS; THEORETICAL STUDY; TURBULENCE; TWO-DIMENSIONAL FLOW;

EID: 79951671296     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010004635     Document Type: Article

References (48)

1. BASDEVANT, C., LEGRAS, B. & SADOURNY, R. 1981 A study ofbarotropic model flows: intermittency, waves and predictability. J. Atmos. Sci. 38, 2305-2326. (Pubitemid 12469648)
2. BATCHELOR, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. II, 233-239.
3. BEWLEY, T. R. 2001 Flow control: new challenges for a renaissance. Prog. Aerosp. Sci. 37, 21-58. (Pubitemid 32875276)
4. BOFFETTA, G. 2007 Energy and enstrophy fluxes in the double cascade oftwo-dimensional turbulence. J. Fluid Mech. 589, 253-260. (Pubitemid 350214589)
5. BOFFETTA, G., CELANI, A., MUSACCHIO, S. & VERGASSOLA, M. 2002 Intermittency in two-dimensional Ekman-Navier-Stokes turbulence. Phys. Rev. E 66, 026304.
6. BOFFETTA, G. & MUSACCHIO, S. 2010 Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82, 016307
7. BORUE, V. 1993 Spectral exponents ofenstrophy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 71, 3967.
8. BRACCO, A. & MCWILLIAMS, J. C. 2010 Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence. J. Fluid Mech. 646, 517-526.
9. BRUNEAU, C. H. & KELLAY, H. 2005 Experiments and direct numerical simulations of two-dimensional turbulence. Phys. Rev. E 71, 046305.
10. CHEN, S., ECKE, R. E., EYINK, G. L., WANG, X. & XIAO, Z. 2003 Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett. 91, 214501.
11. CLERCX, H. J. H. & VAN HEIJST, G. J. F. 2009 Two-dimensional Navier-Stokes turbulence in bounded domains. Appl. Mech. Rev. 62, 020802.
12. CONSTANTIN, P., FOIAS, C. & MANLEY, O. 1994 Effects of the forcing function spectrum on energy spectrum in 2-D turbulence. Phys. Fluids 6, 427-429.
13. EDWARDS, W. S., TUCKERMAN, L. S., FRIESNER, R. A. & SORENSEN, D. C. 1994 Krylov methods for the incompressible Navier-Stokes equations. J. Comp. Phys. 110, 82-102. (Pubitemid 124013346)
14. FJøRTOFT, R. 1953 On the changes in the spectral distribution ofkinetic energy for two dimensional, nondivergent flow. Tellus 5, 225-230.
15. FRISCH, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
16. FRISCH, U. & SULEM, P. L. 1984 Numerical simulation of inverse cascade in two-dimensional turbulence. Phys. Fluids 27, 1921-1923. (Pubitemid 14623870)
17. GAGE, K. S. & NASTROM, G. D. 1985 On the spectrum of the atmospheric velocity fluctuations seen by MST/ST radar and their interpretation. Radio Sci. 20, 1339-1374.
18. GIA, G. & CHAKRABORTY, P. 2006 Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory. Phys. Rev. Lett. 96, 044502.
19. GKIOULEKAS, E. & TUNG, K. K. 2007 A new proof on net upscale energy cascade in two-dimensional and quasi-geostrophic turbulence. J. Fluid Mech. 576, 173-189. (Pubitemid 47039346)
20. GUNZBURGER, M. D. 2003 Perspectives in Flow Control and Optimization. SIAM.
21. KOLMOGOROV, A. K. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. 30, 301-305.
22. KRAICHNAN, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417-1423.
23. KRAICHNAN, R. H. 1971 Inertial-range transfer in two-and three-dimensional turbulence. J. Fluid Mech. 47, 525-535.
24. LEBEDEV, L. P. & VOROVICH, I. I. 2002 Functional Analysis in Mechanics. Springer.
25. LEITH, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671-673.
26. LILLY, D. D. 1969 Numerical simulation of two-dimensional turbulence. Phys. Fluids Suppl. II, 240-249.
27. LiNDBORG, E. 1999 Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259-288.
28. LlONS, J. L. 1969 Contrôle Optimal des Syst̀emes Gouverńes par des Equations aux D́eriv́ees Partielles. Dunod (English translation, Springer).
29. LUNDGREN, T. S. 2003 Linearly forced isotropic turbulence. Center for Turbulence Research Annual Research Briefs, 461-473.
30. MALTRUD, M. E. & VALLIS, G. K. 1993 Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence. Phys. Fluids A 5, 1760-1775.
31. MARTEAU, D., CARDOSO, O. & TABELING, P. 1995 Equilibrium states oftwo-dimensional turbulence: an experimental study. Phys. Rev. E 51, 5124-5127.
32. MERILEES, P. E. & WARN, H. 1975 On energy and enstrophy exchanges in two-dimensional non-divergent flow. J. Fluid Mech. 69, 625-630.
33. NOCEDAL, J. & WRIGHT, S. J. 2000 Numerical Optimization. Springer.
34. PASQUERO, C. & FALKOVICH, G. 2002 Stationary spectrum of vorticity cascade in two-dimensional turbulence. Phys. Rev. E 65, 056305.
35. PROTAS, B., BEWLEY, T. R. & HAGEN, G. 2004 A comprehensive framework for the regularization of adjoint analysis in multiscale PDE systems. J. Comp. Phys. 195, 49-89. (Pubitemid 38354640)
36. ROSALES, C. & MENEVEAU, C. 2005 Linear forcing in numerical simulations ofisotropic turbulence: physical space implementation and convergence studies. Phys. Fluids 17, 095106.
37. SCHORGHOFER, N. 2000 Energy spectra of steady two-dimensional turbulent flows. Phys. Rev. E 61, 6575-6577.
38. Schulze, J. C., Schmid, P. J. & Sesterhenn, J. L. 2009 Exponential time integration using Krylov subspaces. Intl J. Numer. Meth. Fluids 60, 591-609.
39. Scott, R. K. 2007 Non-robustness of the two-dimensional turbulent inverse cascade. Phys. Rev. E 75, 046301.
40. Smith, L. M. & Yakhot, V. 1993 Bose condensation and small-scale structure generation in a random force driven 2D turbulence. Phys. Rev. Lett. 71, 352-355.
41. Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139-168. (Pubitemid 17464126)
42. Tran, C. V. & Bowman, J. C. 2003 On the dual cascade in two dimensional turbulence. Physica D 176, 242-255.
43. Tran, C. V. & Dritschel, D. G. 2006 Vanishing enstrophy dissipation in two-dimensional Navier-Stokes turbulence in the inviscid limit. J. Fluid Mech. 559, 107-116. (Pubitemid 44110520)
44. Tran, C. V., Dritschel, D. G. & Scott, R. K. 2007 Revisiting Batchelor's theory of two-dimensional turbulence. J. Fluid Mech. 591, 379-391.
45. Tran, C. V. & Shepherd, T. G. 2002 Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence. Physica D 165, 199-212. (Pubitemid 34532438)
46. Tsang, Y.-K., Ott, E., Antonsen, T. M. & Guzdar, P. N. 2005 Intermittency in two-dimensional turbulence with drag. Phys. Rev. E 71, 066313.
47. Tsang, Y.-K. & Young, W. R. 2009 Force-dissipative two-dimensional turbulence: a scaling regime controlled by drag. Phys. Rev. E 79, 045308(R).
48. Welch, W. T. & Tung, K. K. 1998 Nonlinear baroclinic adjustment and wavenumber selection in a simple case. J. Atmos. Sci. 55, 1285-1302.