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Title:  Toward a theory of interstellar turbulence. 1: weak alfvenic turbulence 
Authors:  Sridhar, S. Goldreich, P. 
Keywords:  collisionless plasmas incompressible flow incompressible fluids interstellar matter magnetohydrodynamic flow magnetohydrodynamic turbulence magnetohydrodynamic waves radio waves variational principles , energy spectra 
Issue Date:  Sep1994 
Publisher:  The University of Chicago Press for the American Astronomical Society 
Citation:  Astrophysical Journal, 1994, vol.432, p612621 
Abstract:  We study weak Alfvenic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of smallscale turbulence in the interstellar medium. We prove that resonant 3wave interactions are absent. We also show that the IroshnikovKraichnan theory of incompressible, magnetohydrodynamic turbulence  which is widely accepted  describes weak 3wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfven wave and the pseudo Alfven wave. The threedimensional inertialrange energy spectrum of 4wave shear Alfven turbulence guessed from physical arguments reads E(kz, kperpendicular) approximately VAvLL1/3kperpendicular10/3, where VA is the Alfven speed, and vL is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across lambdaperpendicular approximately kperpendicular exp 1 is vlambda (sub perpendicular) is approximately vL(lambdaperpendicular/L)2/3. We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in kspace, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, kperpendicularL is approximately (VA/vL)3/2, weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4wave inertialrange to be substantial. When the excitation is strong, the width of the 4wave inertialrange shrinks to zero. This seems likely to be the case in the interstellar medium. 
Description:  Open Access 
URI:  http://hdl.handle.net/2289/4860 
ISSN:  0004637X 15384357 (Online) 
Alternative Location:  http://adsabs.harvard.edu/doi/10.1086/174600 http://dx.doi.org/10.1086/174600 
Copyright:  1994 American Astronomical Society 
Appears in Collections:  Research Papers (A&A)

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