Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-20T08:05:46.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Nature and dynamics of overreflection of Alfvén waves in MHD shear flows

Published online by Cambridge University Press:  16 May 2014

D. Gogichaishvili ,
G. Chagelishvili ,
R. Chanishvili  and
J. Lominadze
D. Gogichaishvili
Affiliation:
Department of Physics, The University of Texas, Austin, TX 78712, USA
G. Chagelishvili*
Affiliation:
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia Institute of Geophysics, Tbilisi State University, Tbilisi 0193, Georgia
R. Chanishvili
Affiliation:
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia Institute of Geophysics, Tbilisi State University, Tbilisi 0193, Georgia
J. Lominadze
Affiliation:
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0162, Georgia Institute of Geophysics, Tbilisi State University, Tbilisi 0193, Georgia
*
†Email address for correspondence: georgech123@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Our goal is to gain new insights into the physics of wave overreflection phenomenon in magnetohydrodynamic (MHD) nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, U0=(Sy,0,0), that contain two different types of Alfvén waves. These waves are reduced to pseudo- and shear-Alfvén waves when wavenumber along Z-axis equals zero (i.e. when kz=0). Therefore, for simplicity, we labeled these waves as: P-Alfvén and S-Alfvén waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetrically coupled with P-AWs; S-AWs do not participate in the linear dynamics of P-AWs, (3) the transient growth of S-AWs is somewhat smaller compared with that of P-AWs, (4) the linear transient processes are highly anisotropic in wave number space, (5) the waves with small streamwise wavenumbers exhibit stronger transient growth and become more balanced, (6) maximal transient growth (and overreflection) of the wave energy occurs in the two-dimensional case – at zero spanwise wavenumber.

To the end, we analyze nonlinear consequences of the described anisotropic linear dynamics – they should lead to an anisotropy of nonlinear cascade processes significantly changing their essence, pointing to a need of revisiting the existing concepts of cascade processes in MHD shear flows.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 5 , October 2014 , pp. 667 - 685
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baggett, J., Driscoll, T. and Trefethen, L. 1995 A mostly linear model of transition to turbulence. Phys. Fluids 7, 833–538.CrossRefGoogle Scholar
Bakas, N., Ioannou, P. and Kefaliakos, G. 2001 The emergence of coherent structures in stratified shear flow. J. Atmos. Sci. 58, 2790–2806.2.0.CO;2>CrossRefGoogle Scholar
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Boldyrev, S. 2005 On the spectrum of magnetohydrodynamic turbulence. Astrophys. J. Lett. 626, L37–40.Google Scholar
Brandenburg, A. and Lazarian, A. 2013 Astrophysical hydromagnetic turbulence. Space Sci. Rev. 178, 163–200.Google Scholar
Chagelishvili, G., Chanishvili, R. and Lominadze, J. 1996 Physics of the amplification of vortex disturbances in shear flows. JETP Lett. 63, 543–549.Google Scholar
Chagelishvili, G., Chanishvili, R., Lominadze, J. and Tevzadze, A. 1997a Magnetohydrodynamic waves linear evolution in parallel shear flows: amplification and mutual transformations. Phys. Plasmas 5, 259–269.CrossRefGoogle Scholar
Chagelishvili, G., Tevzadze, A., Bodo, G. and Moiseev, S. 1997b Linear mechanism of wave emergence from vortices in smooth shear flows. Phys. Rev. Lett. 79, 3178–3121.Google Scholar
Dmitruk, P., Matthaeus, W., Milano, L., Oughton, S., Zank, G. and Mullan, D. 2002 Coronal heating distribution due to low-frequency, wave-driven turbulence. Astrophisical J. 575, 571–577.Google Scholar
Eckhardt, B., Schneider, T., Hof, B. and Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.Google Scholar
Farrell, B. and Ioannou, P. 1993a Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids A 5, 1390–1400.Google Scholar
Farrell, B. and Ioannou, P. 1993b Stochastic forcing of perturbation variance in unbounded shear and deformation flows. J. Atmos. Sci. 50, 200–211.2.0.CO;2>CrossRefGoogle Scholar
Goldreich, P. and Sridhar, S. 1995 Toward a theory of interstellar turbulence. 2. Strong alfvenic turbulence. Astrophysical J. 438, 763–775.Google Scholar
Goldreich, P. and Tremaine, S. 1978 The excitation and evolution of density waves. Astrophysical J. 222, 850–858.Google Scholar
Goldreich, P. and Tremaine, S. 1979 The excitation of density waves at the lindblad and corotation resonances by an external potential. Astrophysical J. 233, 857–871.CrossRefGoogle Scholar
Grossmann, S. 2000 The onset of shear flow turbulence. Rev. Mod. Phys. 72, 603–618.Google Scholar
Heinemann, M. and Olbert, S. 1980 Non-wkb Alfvén waves in the solar wind. J. Geophys. Res.: Space Phys. 85, 1311–1327.Google Scholar
Hollweg, J. and Kaghashvili, E. 2012 Alfvén waves in shear flows revisited. Astrophysical J. 744, 114–118.Google Scholar
Hollweg, J., Kaghashvili, E. and Chandran, B. 2013 Velocity-shear induced mode coupling in the solar atmospere and solar wind: implication for plasma heating and mhd turbulence. Astrophisical J. 769, 142–152.CrossRefGoogle Scholar
Horton, W., Kim, J.-H., Chagelishvili, G., Bowman, J. and Lominadze, J. 2010 Angular redistribution of nonlinear perturbations: a universal feature of nonuniform flows. Phys. Rev. E. 81, id. 066304.Google Scholar
Iroshnikov, P. 1963 Turbulence of a conducting fluid in a strong magnetic field. Sov. Astron. 7, 566–571.Google Scholar
Kraichnan, R. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387.Google Scholar
Lindzen, R. S. and Barker, J. 1985 Instability and wave over-reflection in stably stratified shear flow. J. Fluid Mech. 151, 189–217.CrossRefGoogle Scholar
Mamatsashvili, G., Gogichaishvili, D., Chagelishvili, G. and Horton, W. 2014 Nonlinear transverse cascade and two-dimensional MHD subcritical turbulence in plane shear flows. Phys. Rev. E 89, 043101.CrossRefGoogle ScholarPubMed
Matthaeus, W., Zank, G., Oughton, S., Mullan, D. and Dmitruk, P. 1999 Coronal heating by magnetohydrodynamic turbulence driven by reflected low-frequency waves. Astrophisical J. 523, L93–96.Google Scholar
Mininni, P. D. 2011 Scale interactions in magnetohydrodynamic turbulence. Annu. Rev. Fluid Mech. 43, 377–397.Google Scholar
Moffatt, H. K. 1967 The interaction of turbulence with strong wind shear. In: Atmospheric Turbulence and Radio Wave Propagation (ed. Yaglom, A. M. and Tatarski, V. I.). Moscow: Nauka, pp. 139–156.Google Scholar
Perez, J. and Chandran, B. 2013 Direct numerical simulations of reflection-driven, mhd turbulence from the sun to the alfvén critical point. Astrophisical J. 776, 124–140.Google Scholar
Reddy, S. and Henningson, D. 1993 Energy growth in viscous channel flows. J. Fluid Mech. 252, 209–238.Google Scholar
Schmid, P. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.Google Scholar
Stepanyants, Yu. and Fabrikant, A. 1989 Reviews of topical problems: propagation of waves in hydrodynamic shear flows. Sov. Phys. Usp. 32, 783–805.Google Scholar
Trefethen, L., Trefethen, A., Reddy, S. and Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Velli, M., Grappin, R. and Mangeney, A. 1989 Turbulenct cascade of incompressible unidirectional alfvén waves in the interplanetary medium. Phys. Rev. Lett. 63, 1807–1810.CrossRefGoogle ScholarPubMed
Verdini, A., Grappin, R., Pinto, R. and Velli, M. 2012 On the origin of the 1/f spectrum in the solar wind magnetic field. Astrophisical J. Lett. 750, L33–37.CrossRefGoogle Scholar
Webb, G., Zank, G., Kaghashvili, E. and Ratkiewicz, R. 2005 Magnetohydrodynamic waves in non-uniform flows i: a variational approach. J. Plasma Phys. 71, 785–809.Google Scholar
Yoshida, Z. 2005 Kinetic theory for non-hermitian dynamics of waves in shear flow. Phys. Plasmas 12, 024503-024503-3.CrossRefGoogle Scholar
Zaqarashvili, T. 2000 Parametric resonance in ideal magnetohydrodynamics. Phys. Rev. E 62, 2745–2753.Google Scholar
Zaqarashvili, T. and Roberts, B. 2002 Swing wave-wave interaction: coupling between fast magnetosonic and Alfvén waves. Phys. Rev. E 66, id. 026401.CrossRefGoogle ScholarPubMed