On WKB expansions for Alfven waves in the solar wind

Journal Article · Sat Sep 01 04:00:00 EDT 1990 · Journal of Geophysical Research; (United States)

DOI:https://doi.org/10.1029/JA095iA09p14873· OSTI ID:5314364

Hollweg, J V ^[1]

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1. Univ. of New Hampshire, Durham (USA)

The author reexamines the WKB expansion for toroidal Alfven waves in the solar wind, as described by equations (9) of Heinemann and Olbert (1980). His principal conclusions are as follows: (1) The WKB expansion used by Belcher (1971) and Hollweg (1973) is nonuniformly convergent. (2) Using the method of multiple scales (Nayfeh, 1981), he obtains an expansion which is uniform. (3) The uniform expansion takes into account the small modification to the Alfven wave phase speed due to spatial gradients of the background. (4) Both the uniform and nonuniform expansions reveal that each normal mode has both Elsaesser variables {delta}z{sup +} {ne} 0 and {delta}z{sup {minus}} {ne} 0. Thus if {delta}z{sup {minus}} corresponds to the outgoing mode in a homogeneous background, an observation of {delta}z{sup +} {ne} 0 does not necessarily imply the presence of the inward propagating mode, as is commonly assumed. (5) Even at the Alfven critical point (where V = {upsilon}{sub A}) he finds that {delta}z{sup +} {ne} 0. Thus incompressible MHD turbulence, which requires both {delta}z{sup +} {ne} 0 and {delta}z{sup {minus}} {ne} 0, can proceed at the Alfven critical point (cf. Roberts, 1989). (6) With very few exceptions, the predictions of these calculations do not agree with recent observations (Marsch and Tu, 1990) of the power spectra of {delta}z{sup +} and {delta}z{sup {minus}} in the solar wind. Thus the evolution of Alfven waves in the solar wind is governed by dynamics not included in the Heinemann and Olbert equations.

• OSTI ID: 5314364
• Journal Information: Journal of Geophysical Research; (United States), Journal Name: Journal of Geophysical Research; (United States) Vol. 95:A9; ISSN JGREA; ISSN 0148-0227
• Country of Publication: United States
• Language: English

Related Subjects

640104* -- Astrophysics & Cosmology-- Solar Phenomena
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALFVEN WAVES
CALCULATION METHODS
COMPARATIVE EVALUATIONS
CONVERGENCE
EVALUATION
EXPANSION
FLUCTUATIONS
FLUID MECHANICS
HYDRODYNAMICS
HYDROMAGNETIC WAVES
MAGNETOHYDRODYNAMICS
MAIN SEQUENCE STARS
MECHANICS
SOLAR ACTIVITY
SOLAR WIND
STARS
SUN
TURBULENCE
VARIATIONS
WAVE PROPAGATION
WKB APPROXIMATION