"Maximum" entropy production in self-organized plasma boundary layer: A thermodynamic discussion about turbulent heat transport

Physics of Plasmas

Volumn 15, Issue 3, 2008, Pages

  Yoshida, Z ^a   Mahajan, S M ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; ENTROPY; HEAT TRANSFER;

ENTROPY PRODUCTION; INVERSE CASCADE; TURBULENT HEAT TRANSPORT;

PLASMAS;

EID: 41549169180     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2890189     Document Type: Article

References (13)

1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems-From Dissipative Structures to Order through Fluctuations (Wiley, New York, 1977).
2. G. W. Paltridge, Q. J. R. Meteorol. Soc. 0035-9009 10.1256/smsqj.42905 101, 475 (1975); G. W. Paltridge, Nature (London) 279, 630 (1979).
3. P. H. Wyant, A. Mongroo, and S. Hameed, J. Atmos. Sci. 45, 189 (1988).
4. H. Grassl, Q. J. R. Meteorol. Soc. 107, 153 (1990).
5. S. Shimozawa and H. Ozawa, Q. J. R. Meteorol. Soc. 128, 2115 (2002).
6. R. D. Lorenz, J. I. Lunine, and P. G. Withers, Geophys. Res. Lett. 28, 415, DOI: 10.1029/2000GL012336 (2001).
7. H. Ozawa, S. Shimokawa, and H. Sakuma, Phys. Rev. E 64, 026303 (2001).
8. R. Dewar, J. Phys. A 36, 631 (2003).
9. F. Wagner, G. Becker, K. Behringer, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.49.1408 49, 1408 (1982); ASDEX Team, Nucl. Fusion 0029-5515 29, 1959 (1989); R. J. Taylor, M. L. Brown, B. D. Fried, H. Grote, J. R. Liberati, G. J. Morales, P. Pribyl, D. Darrow, and M. Ono, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.63.2365 63, 2365 (1989); R. J. Groebner, K. H. Burrell, and R. P. Seraydarian, Phys. Rev. Lett. 64, 3015 (1990).
10. Here, the "minimum" means that S i =0 (so that W =0), but not minimizing S D with examining the relation between the distributions of the temperature T, heat flux f, and the diffusion coefficient. For a critical analysis of "minimum entropy production" in a fluid system, see E. Barbera, Continuum Mech. Thermodyn. 11, 327 (1999).
11. A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 59, 1581 (1987).
12. A. Hasegawa, Adv. Phys. 34, 1 (1985).
13. Examples of a pair of dual variational principles are: (1) for a fixed perimeter, find a curve that maximizes the area of its enclosed region (isoperimetric problem), (2) for a fixed area, find a curve that minimize the perimeter. Note that the opposite problems are "ill-posed": (1') for a fixed perimeter, find a curve that minimizes the area of its enclosed region, (2') for a fixed area, find a curve that maximized the perimeter. To formulate a well-posed variational principle, the target functional to be maximized (minimized) must be "higher-order" ("lower-order") in comparison to the functional representing the constraint. In a variational principle of field theory, "higher-order" means that the functional includes higher-order derivatives. The enstrophy is higher-order with respect to the energy; see Z. Yoshida and S. M. Mahajan, Phys. Rev. Lett. 88, 095001 (2002).