TOWARD A THEORY OF INTERSTELLAR TURBULENCE .2. STRONG ALFVENIC TURBULENCE

We continue to investigate the possibility that interstellar turbulenc e is caused by nonlinear interactions among shear Alfven waves. Here, as in Paper I, we restrict attention to the symmetric case where the o ppositely directed waves carry equal energy fluxes. This precludes app lication to the solar wind in which the outward flux significantly exc eeds the ingoing one. All our detailed calculations are carried out fo r an incompressible magnetized fluid. In incompressible magnetohydrody namics (MHD), nonlinear interactions only occur between oppositely dir ect waves. Paper I contains a detailed derivation of the inertial rang e spectrum for the weak turbulence of shear Alfven waves. As energy ca scades to high perpendicular wavenumbers, interactions become so stron g that the assumption of weakness is no longer valid. Here, we present a theory for the strong turbulence of shear Alfven 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(perpendicular to), are relat ed by k(z) approximate to k(perpendicular to) (2/3)L(-1/3), where L is the outer scale of the turbulence. (3) The ''one-dimensional'' energy spectrum is proportional to k(perpendicular to)(-5/3)-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific e ntropy as a passive contaminant. This gives rise to an electron densit y power spectrum whose form mimics the energy spectrum of the turbulen ce. Radio wave scattering by these electron density fluctuations produ ces anisotropic scatter-broadened images. Damping by ion-neutral colli sions restricts Alfvenic turbulence to highly ionized regions of the i nterstellar medium. We expect negligible generation of compressive MHD waves by shear Alfven waves belonging to the critically balanced casc ade. Viscous and collisionless damping are also unimportant in the int erstellar medium (ISM). Our calculations support the general picture o f interstellar turbulence advanced by Higdon.