Decay of magnetohydrodynamic turbulence from power-law initial conditions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 4 2, 2004, Pages

  Kalelkar, Chirag ^a   Pandit, Rahul ^a,b  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ENERGY ABSORPTION; KINETIC ENERGY; MAGNETIC FIELDS; MATHEMATICAL MODELS; NUMERICAL METHODS; PRESSURE EFFECTS; TURBULENCE; VISCOSITY; WIND TUNNELS;

DIRECT NUMERICAL SIMULATIONS (DNS); ENERGY-DECAY EXPONENTS; MAGNETIC HELICITY; POWER-LAW INITIAL CONDITIONS;

MAGNETOHYDRODYNAMICS;

EID: 42749106971     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. G. Taylor, Proc. R. Soc. London, Ser. A 151, 421 (1935); A. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941); Proc. R. Soc. London, Ser. A 434, 15 (1991); P. Saffman, Phys. Fluids 10, 1349 (1967).
2. G. Taylor, Proc. R. Soc. London, Ser. A 151, 421 (1935); A. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941); Proc. R. Soc. London, Ser. A 434, 15 (1991); P. Saffman, Phys. Fluids 10, 1349 (1967).
3. G. Taylor, Proc. R. Soc. London, Ser. A 151, 421 (1935); A. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941); Proc. R. Soc. London, Ser. A 434, 15 (1991); P. Saffman, Phys. Fluids 10, 1349 (1967).
4. G. Taylor, Proc. R. Soc. London, Ser. A 151, 421 (1935); A. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941); Proc. R. Soc. London, Ser. A 434, 15 (1991); P. Saffman, Phys. Fluids 10, 1349 (1967).
5. A. Monin and A. Yaglom, Statistical Fluid Mechanics, edited by J. Lumley (MIT Press, Cambridge, 1975), Vol. 2.
6. G. Comte-Bellot and S. Corrsin, J. Fluid Mech. 25, 657 (1966).
7. M. Smith, R. Donnelly, N. Goldenfeld, and W. Vinen, Phys. Rev. Lett. 71, 16 (1993).
8. M. Uberoi and S. Wallis, Phys. Fluids 10, 6 (1967); M. Mohamed and J. LaRue, J. Fluid Mech. 219, 195 (1990).
9. M. Uberoi and S. Wallis, Phys. Fluids 10, 6 (1967); M. Mohamed and J. LaRue, J. Fluid Mech. 219, 195 (1990).
10. W. George, Phys. Fluids A 4, 7 (1992).
11. P. Ditlevsen, M. Jensen, and P. Olesen, e-print nlin.CD/ 0205055.
12. P. Olesen, Phys. Lett. B 398, 321 (1997).
13. D. Biskamp and W. Müller, Phys. Rev. Lett. 83, 2195 (1999); M. Christensson, M. Hindmarsh, and A. Brandenburg, Phys. Rev. E 64, 056405 (2001).
14. D. Biskamp and W. Müller, Phys. Rev. Lett. 83, 2195 (1999); M. Christensson, M. Hindmarsh, and A. Brandenburg, Phys. Rev. E 64, 056405 (2001).
15. We restrict ourselves to statistical invariance under rotations but not necessarily under reflections.
16. A. Brandenburg, K. Enqvist, and P. Olesen, Phys. Rev. D 54, 1291 (1996); P. Frick and D. Sokoloff, Phys. Rev. E 57, 4155 (1998).
17. A. Brandenburg, K. Enqvist, and P. Olesen, Phys. Rev. D 54, 1291 (1996); P. Frick and D. Sokoloff, Phys. Rev. E 57, 4155 (1998).
18. A. Basu, A. Sain, S. Dhar, and R. Pandit, Phys. Rev. Lett. 81, 2687 (1998).
19. The energy densities decay exponentially at large wave numbers in the far-dissipation range. We have therefore assumed convergence of the integrals appearing in Eqs. (11)-(14), which appears reasonable considering the presence of a naturally occurring viscous cutoff at large wave numbers.
20. E. Gledzer, Sov. Phys. Dokl. 18, 216 (1973); K. Ohkitani and M. Yamada, Prog. Theor. Phys. 81, 329 (1989); L. Kadanoff, D. Lohse, J. Wang, and R. Benzi, Phys. Fluids 7, 517 (1995).
21. E. Gledzer, Sov. Phys. Dokl. 18, 216 (1973); K. Ohkitani and M. Yamada, Prog. Theor. Phys. 81, 329 (1989); L. Kadanoff, D. Lohse, J. Wang, and R. Benzi, Phys. Fluids 7, 517 (1995).
22. E. Gledzer, Sov. Phys. Dokl. 18, 216 (1973); K. Ohkitani and M. Yamada, Prog. Theor. Phys. 81, 329 (1989); L. Kadanoff, D. Lohse, J. Wang, and R. Benzi, Phys. Fluids 7, 517 (1995).
23. There is a typographical error in the equations given in Ref. [12]. This does not affect their results. We have corrected this error in Eq. (15).
24. D. Pisarenko, L. Biferale, D. Courvoisier, U. Frisch, and M. Vergassola, Phys. Fluids A 5, 10 (1993).
25. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1996).
26. S. Dhar, A. Sain, and R. Pandit, Phys. Rev. Lett. 78, 2964 (1997).
27. W. Heisenberg, Proc. R. Soc. London, Ser. A 195, 402 (1948).
28. V. L'vov, R. Pasmanter, A. Pomyalov, and I. Proccacia, Phys. Rev. E 67, 066310 (2003).