Viscous model of solar wind flow

Dahlberg, E.

doi:10.1029/ja075i031p06312

Cited by 10 publications

(4 citation statements)

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“…The rather small effects of viscosity (due to Coulomb collisions) have been considered in Navier-Stokes approximations of the hydrodynamic momentum equations (Scarf and Noble 1965;Whang et al 1966;Konyukov 1969;Eisler 1969;Dahlberg 1970). Time-dependent hydrodynamic models of the solar wind expansion have also been developed.…”

Section: The First Hydrodynamic Model Of the Solar Windmentioning

confidence: 99%

A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

2010

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The paper reviews the main advantages and limitations of the kinetic exospheric and fluid models of the solar wind (SW). The general theoretical background is outlined: the Boltzmann and Fokker-Planck equations, the Liouville and Vlasov equations, the plasma transport equations derived from an ''equation of change''. The paper provides a brief history of the solar wind modeling. It discusses the hydrostatic model imagined by Chapman, the first supersonic hydrodynamic models published by Parker and the first generation subsonic kinetic model proposed by Chamberlain. It is shown that a correct estimation of the electric field, as in the second generation kinetic exospheric models developed by Lemaire and Scherer, provides a supersonic expansion of the corona, reconciling the hydrodynamic and the kinetic approach. The modern developments are also reviewed emphasizing the characteristics of several generations of kinetic exospheric and multi-fluid models. The third generation kinetic exospheric models consider kappa velocity distribution function (VDF) instead of a Maxwellian at the exobase and in addition they treat a non-monotonic variation of the electric potential with the radial distance; the fourth generation exospheric models include Coulomb collisions based on the Fokker-Planck collision term. Multi-fluid models of the solar wind provide a coarse grained description of the system and reproduce with success the spatio-temporal variation of SW macroscopic properties (density, bulk velocity). The main categories of multi-fluid SW models are reviewed: the 5-moment, or Euler, models, originally proposed by Parker to describe the supersonic SW expansion; the 8-moment and 16-moment fluid models, the gyrotropic 123Surv ) 32:1-70 DOI 10.1007 approach with improved collision terms as well as the gyrotropic models based on observed VDFs. The outstanding problem of collisions, including the long range Coulomb encounters, is also discussed, both in the kinetic and multi-fluid context. Although for decades the two approaches have been seen as opposed, in this paper we emphasize their complementarity. The review of the kinetic and fluid models of the solar wind contributes also to a better evaluation of the open questions still existent in SW modeling and suggests possible future developments.

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Section: The First Hydrodynamic Model Of the Solar Windmentioning

confidence: 99%

A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

2010

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“…The analysis of § 3 with regard to a perturbation of the Whang & Chang solution is particularly fruitful in th a t the connection between the Whang &Chang (1965) andW hang et al (1966) solutions is derived, and the uniform validity of the controversial r~% tem perature variation established. Eisler (1969) appeared to claim uniqueness for the Whang et al viscous solution (41), but Dahlberg (1970) challenged this and p u t forward his solution (43) characterized for large r by tem perature variation oc r~$. (It is a simple m atter to check from equations ( 6), ( 7) th a t the only supersonic viscous ( 0) solutions are indeed those characterized by the x% tem perature behaviours as x-> 0.)…”

Section: Discussionmentioning

confidence: 99%

“…This is actually a simple procedure for the expansions ( 9) then tu rn out to be none other than a rearrangement of the viscous solution obtained by Dahlberg (1970),…”

Section: (A) Parker Solutionmentioning

confidence: 99%

“…10-2) can at best be an approximation, and it will be seen th a t the inclusion of viscous terms has considerable effect on the structure of the solutions far from the Sun. Further, the relation between the three well known inviscid supersonic solutions of Parker (1964), Whang & Chang (1965), and Durney (1971) (characterized respectively by tem pera ture T oc , r~*, r~* as radial distance r -> 00) and the two viscous solutions of Whang, Liu & Chang (1966) and Dahlberg (1970) (characterized by oc r~%, r~ § as co) will be clarified.lt should be emphasized th a t the present study is pri marily to analyse the mathematical properties and implications of the (idealized) viscous solar wind equations rather than to attem pt to model the real solar wind per se.…”

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On the effects of viscosity in one-fluid solar wind theory

Summers

1976

Proc. R. Soc. Lond. A

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In order to examine the influence of small viscous effects on the in viscid solutions of Parker, Whang & Chang, and Durney the ideal, steady, one-fluid solar wind equations are examined in the limit: Reynolds number → ∞, Prandtl number → 0 (i. e. viscosity → 0, thermal conduction fixed). The method of matched asymptotic expansions is employed, and it is found that the inclusion of viscosity has considerable effect on the solutions far from the Sun. Small viscous terms cause the velocity to drop below the supersonic value of the Parker solution to subsonic values through a diffuse shock, the temperature still following the variation ∝ r -2/7 at large distances r . The result of small viscous effects on the Whang & Chang solution is that the temperature changes from a variation ∝ r -2/5 to follow the r -2/3 law of Whang, Liu & Chang, the velocity remaining supersonic, as r → ∞. The Durney solution is found to be the leading order part of a solution that is uniformly valid as r → ∞ in the limit considered.

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Concluding Remarks

Hundhausen

1972

Coronal Expansion and Solar Wind

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Viscous model of solar wind flow

Cited by 10 publications

References 5 publications

A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

On the effects of viscosity in one-fluid solar wind theory

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