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8
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0142051275
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Coronal heating and reduced MHD
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edited by E. Falgarone and T. Passot (Springer, New York)
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S. Oughton, P. Dmitruk, and W. H. Matthaeus, Coronal heating and reduced MHD, in Turbulence and Magnetic Fields in Astrophysics, edited by E. Falgarone and T. Passot (Springer, New York, 2003), Vol. 614, pp. 28-55.
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Oughton, S.1
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15
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2942617156
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See Zank and Matthaeus (Ref. 6) for discussion of difficulties associated with derivations based on the incompressible MHD equations
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See Zank and Matthaeus (Ref. 6) for discussion of difficulties associated with derivations based on the incompressible MHD equations.
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19
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2942562727
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note
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λz(k), the "Nonlinearity parameter." See also Sec. V.
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21
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0032493990
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W. H. Matthaeus, S. Oughton, S. Ghosh, and M. Hossain, Phys. Rev. Lett. 81, 2056 (1998).
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22
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10644273917
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Nonlinear Alfvén waves. I. Interactions between outgoing and ingoing Alfvén waves according to an amplitude expansion
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to be published
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B. J. Vasquez and J. V. Hollweg, "Nonlinear Alfvén waves. I. Interactions between outgoing and ingoing Alfvén waves according to an amplitude expansion," J. Geophys. Res. (to be published).
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J. Geophys. Res.
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Vasquez, B.J.1
Hollweg, J.V.2
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23
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41749120980
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Nonlinear Alfvén waves. II. The influence of wave advection and finite wavelength effects
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to be published
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B. J. Vasquez, S. A. Markovskii, and J. V. Hollweg, "Nonlinear Alfvén waves. II. The influence of wave advection and finite wavelength effects," J. Geophys. Res. (to be published).
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J. Geophys. Res.
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Vasquez, B.J.1
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32
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2942585570
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note
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0 small but nonzero, where linear and nonlinear effects will be of comparable magnitude. The direction of flow of excitations in k-space across this transition region is one of the major unanswered questions remaining."
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39
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0000640106
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W. H. Matthaeus, S. Ghosh, S. Oughton, and D. A. Roberts, J. Geophys. Res. 101, 7619 (1996).
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41
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2942622565
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note
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Note that there are difficulties associated with wavepacket decompositions of space-filling turbulence. For example, although there is an aspect of super-position connected with the decomposition, it cannot be a linear super-position since turbulence is nonlinear. Additionally, wavepackets should typically be spatially well-separated, and typically maintain at least some semblance of coherence after two of them interact. We are not aware of any work in which such wavepacket behavior has been identified or tracked.
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42
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2942538427
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note
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1 = 0. This is sometimes refered to as "trivial resonance."
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43
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2942525854
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Provided boundary conditions allow. See Appendix C and Ref. 56
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Provided boundary conditions allow. See Appendix C and Ref. 56.
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44
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0000000898
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P. S. Iroshnikov, Astron. Zh. 40, 742 (1963) [Sov. Astron 7, 566 (1964)].
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Iroshnikov, P.S.1
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45
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0000665785
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P. S. Iroshnikov, Astron. Zh. 40, 742 (1963) [Sov. Astron 7, 566 (1964)].
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48
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0012662008
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World Scientific, Singapore, Lecture Notes from the NCAR-GTP Summer School, June 1987
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D. C. Montgomery, Lecture Notes on Turbulence (World Scientific, Singapore, 1989), p. 75, Lecture Notes from the NCAR-GTP Summer School, June 1987.
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Montgomery, D.C.1
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49
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2942531031
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note
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Note that the quasi-resonance condition given as Eq. (11) is not applicable for H-H interactions since for these modes the amplitudes A± cannot be treated as slowly varying.
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50
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2942626146
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note
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diss is sufficiently large [Fig. 1(b)].
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51
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0035836884
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S. Oughton, W. H. Matthaeus, P. Dmitruk, L. M. Milano, G. P. Zank, and D. J. Mullan, Astrophys. J. 551, 565 (2001).
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Zank, G.P.5
Mullan, D.J.6
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52
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2942534682
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note
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- summed over p,q subject to k=p+q.
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53
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2942532879
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note
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A(k), although not too much so.
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56
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18244420829
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S. V, Nazarenko, A. C. Newell, and S. Galtier, Physica D 152-153, 646 (2001).
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Nazarenko, S.V.1
Newell, A.C.2
Galtier, S.3
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57
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0035335046
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P. Dmitruk, W. H. Matthaeus, L. J. Milano, and S. Oughton, Phys. Plasmas 8, 2377 (2001).
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Phys. Plasmas
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Dmitruk, P.1
Matthaeus, W.H.2
Milano, L.J.3
Oughton, S.4
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58
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0033588651
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W. H. Matthaeus, G. P. Zank, S. Oughton, D. J. Mullan, and P. Dmitruk, Astrophys. J. Lett. 523, L93 (1999).
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Matthaeus, W.H.1
Zank, G.P.2
Oughton, S.3
Mullan, D.J.4
Dmitruk, P.5
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60
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0035365774
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L. J. Milano, W. H. Matthaeus, P. Dmitruk, and D. C. Montgomery, Phys. Plasmas 8, 2673 (2001).
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Phys. Plasmas
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Milano, L.J.1
Matthaeus, W.H.2
Dmitruk, P.3
Montgomery, D.C.4
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