Magnetohydrodynamic drift equations: From Langmuir circulations to magnetohydrodynamic dynamo?

Journal of Fluid Mechanics

Volumn 698, Issue , 2012, Pages 51-61

  Vladimirov, V A ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

dynamo theory; general fluid mechanics; magnetohydrodynamics

Indexed keywords

FLUID MECHANICS; INTERACTIVE DEVICES; INVERSE PROBLEMS; OSCILLATING FLOW; REYNOLDS NUMBER; VELOCITY;

ASYMPTOTIC THEORIES; DYNAMO THEORIES; GENERAL FLUID MECHANICS; LANGMUIR CIRCULATIONS; MAGNETOHYDRODYNAMIC EQUATIONS; MATHEMATICAL APPROACH; MATHEMATICAL STRUCTURE; POSSIBLE MECHANISMS;

MAGNETOHYDRODYNAMICS;

EQUATION; FLOW VELOCITY; FLUID MECHANICS; GEODYNAMO; LANGMUIR CIRCULATION; MAGNETIC FIELD; MAGNETOHYDRODYNAMICS; NUMERICAL METHOD;

EID: 84859977826     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.40     Document Type: Article

References (32)

1. ANDREWS, D. & MCINTYRE, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609-646. (Pubitemid 9413277)
2. BATCHELOR, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
3. CHILDRESS, S. & GILBERT, A. D. 1995 Stretch, Twist, Fold: The Fast Dynamo. Springer.
4. CRAIK, A. D. D. 1982 The drift velocity of water waves. J. Fluid Mech. 116, 187-205.
5. CRAIK, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
6. CRAIK, A. D. D. & LEIBOVICH, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (3), 401-426.
7. DEBNATH, L. 1994 Nonlinear Water Waves. Academic Press.
8. FRISCH, U. 1985 Turbulence. The Legacy of A. N. Kolmogorov. Cambridge University Press.
9. HERREMAN, W. & LESAFFRE, P. 2011 Stokes drift dynamos. J. Fluid Mech. 679 (3), 32-57.
10. HUGHES, D. W. & PROCTOR, M. R. E. 2010 Turbulent magnetic diffusivity tensor for time-dependent mean fields. Phys. Rev. Lett. 104, 024503.
11. ILIN, K. I. & MORGULIS, A. B. 2011 Steady streaming between two vibrating planes at high Reynolds numbers. Phys. Fluid Dyn., arXiv:1108.2710v1.
12. KEVORKIAN, J. & COLE, J. D. 1996 Multiple Scale and Singular Perturbation Method, Applied Mathematical Sciences, vol. 114, Springer.
13. LAMB, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
14. LEIBOVICH, S. 1983 The forms and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391-427.
15. LONGUET-HIGGINS, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535-581.
16. MOFFATT, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluid. Cambridge University Press.
17. MOFFATT, H. K. 1983 Transport effects associated with turbulence with particular attention to the influence of helicity. Rep. Prog. Phys. 46, 621-664.
18. NAYFEH, A. H. 1973 Perturbation Methods. John Wiley & Sons.
19. RILEY, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43-65.
20. ROBERTS, P. H. & SOWARD, A. M. 1992 Dynamo theory. Annu. Rev. Fluid Mech. 24, 459-512.
21. SOWARD, A. M. & ROBERTS, P. H. 2010 The hybrid Euler-Lagrange procedure using an extension of Moffatt's method. J. Fluid Mech. 661, 45-72.
22. STOKES, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441-455 (reprinted in Mathematical and Physical Papers, vol. 1, pp. 197-219).
23. THORPE, S. A. 2004 Langmuir circulation. Annu. Rev. Fluid Mech. 36, 55-79. (Pubitemid 38381904)
24. VLADIMIROV, V. A. 1985a An example of equivalence between density stratification and rotation. Sov. Phys. Dokl. 30 (9), 748-750 (translated from Russian).
25. VLADIMIROV, V. A. 1985b Analogy between the effects of density stratification and rotation. J. Appl. Mech. Tech. Phys. 26 (3), 353-362 (translated from Russian). (Pubitemid 16569365)
26. VLADIMIROV, V. A. 2005 Vibrodynamics of pendulum and submerged solid. J. Math. Fluid Mech. 7, S397-S412.
27. VLADIMIROV, V. A. 2008 Viscous flows in a half-space caused by tangential vibrations on its boundary. Stud. Appl. Maths 121 (4), 337-367.
28. VLADIMIROV, V. A. 2010 Admixture and drift in oscillating fluid flows. Phys. Fluid Dyn., arXiv:1009.4085v1.
29. VLADIMIROV, V. A. 2011 Theory of non-degenerate oscillatory flows. Phys. Fluid Dyn., arXiv:1110.3633v2.
30. VLADIMIROV, V. A., MOFFATT, H. K. & ILIN, K. I. 1996 On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 2. Stability criteria for two-dimensional flows. J. Fluid Mech. 329, 187-207
31. YUDOVICH, V. I. 2006 Vibrodynamics and vibrogeometry of mechanical systems with constraints (in Russian). Usp. Mekh. 4 (3), 26-158.
32. ZHELIGOVSKY, V. A. 2009 Mathematical Stability Theory for MHD Flows with Respect to Long-Wave Perturbations. Krasand (in Russian).