Toward a theory of interstellar turbulence. II. Strong Alfvénic turbulence

Abstract

We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfvén waves. Here, as in Paper I, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. Paper I contains a detailed derivation of the inertial range spectrum for the weak turbulence of shear Alfvén waves. As energy cascades to high perpendicular wavenumbers, interactions become so strong that the assumption of weakness is no longer valid. Here, we present a theory for the strong turbulence of shear Alfvén waves. It has the following main characteristics. (1) The inertial-range energy spectrum exhibits a critical balance beween linear wave periods and nonlinear turnover timescales. (2) The "eddies" are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k_z and k_⊥, are related by k_z ≈ k^(2/3) _⊥L^(-1/3), where L is the outer scale of the turbulence. (3) The "one-dimensional" energy spectrum is proportional to k^(-5/3) _⊥-an anisotropic Kolmogorov energy spectrum. Shear Alfvénic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio, wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvénic turbulence to highly ionized regions of the interstellar medium. We expect negligible generation of compressive MHD waves by shear Alfvén waves belonging to the critically balanced cascade. Viscous and collisionless damping are also unimportant in the interstellar medium (ISM). Our calculations support the general picture of interstellar turbulence advanced by Higdon.