By unknown

ISBN-10: 0387267425

ISBN-13: 9780387267425

This ebook is of curiosity to researchers in astrophysics and the planetary sciences. It surveys the present wisdom at the propagation of nonlinear waves and the advance of a turbulent dynamics in magnetohydrodynamic flows. The authors emphasize how the theoretical knowing of MHD waves and turbulence is said to the outline of media the place the presence of an ambient magnetic box is understood to play a vital function. those results are vital within the physics of varied area plasmas corresponding to the magnetosphere, the sunlight wind, the sunlight corona, the interplanetary and interstellar media, and so forth. The authors deal with primary features as published by way of asymptotic research, numerical simulations, and observations within the sunlight wind.

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**Extra info for Nonlinear MHD Waves and Turbulence**

**Example text**

Then a small parameter µ originates in the assumptions characterizing density variations (ν ∼ µ2 , ∂r ln ν ∼ µ). Assume that the wave beam and, therefore, ν vanish at ∞. Then we can argue in a way similar to that one ¯ m ∼ µ2 ∂ 2 F¯m . in the plane case. From Eq. (93) we ﬁnd that inside the beam G ρ ¯ m in Eq. (92) as small inside the Due to that, we consider the terms with G beam and neglect them (in the lowest approximation). Likewise, in Eq. (63) we can neglect both terms with G and Ez . Then Eq.

42. Shukla P. , 1989a, Astrophys. , 155, 145. 43. Shukla P. , & Stenﬂo, 1989b, Phys. Fluids B, 1, 1926. 44. Shukla P. , & Varma R. , 1993, Phys. Fluids B, 5, 236. 45. Shukla P. , 1995, Physica Scripta, T60, 32. 46. Shukla P. , Birk G. , 1996, Plasma Phys. , 22, 818. 47. Shukla P. , 1998a, Phys. Lett. A, 239, 369. 48. Shukla P. , Mirza A. , & Faria Jr. R. , 1998b, Phys. Plasmas, 5, 616. 49. Shukla P. , & Bingham, 1999a, Phys. Plasmas, 6, in press. 50. Shukla P. , McKenzie J. , & Axford W. , 184, in press.

80). Therefore, Eqs. (81) and DN = κΠE with Π ≈ (1/2)|F |2 lead to the same results as the ponderomotive nolinearities with the density variation (63). This is in agreement with the results obtained (by means of another approach) for the slab solitons in gyrotropic media, which are not necessarily plasmas [12]. The gyrotropic properties for such matherials are determinened by the parameter g that is called “the gyrotropic parameter”. {The basic equations of the linear theory [19] can be reduced to the linear part of Eq.

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