Scale-dependent dynamic alignment and inertial-range spectral index in solar wind turbulence*

The power spectra of velocity and magnetic fluctuations in the solar wind has long been associated with an incompressible Magnetohydrodynamics (MHD) turbulent cascade mediated by Alfv'en-like fluctuations. A major development in MHD turbulence theory was Boldyrev's suggestion that as energy cascades from large to small scales in the inertial range, velocity and magnetic fluctuations develop a scale-dependent dynamic alignment (SDDA) that leads to a reduction of the nonlinear interactions and a three-dimensional anisotropy. Most phenomenological models of strong MHD turbulence have in common Goldreich and Sridhar's assumption of critical balance, i.e., that the time scale associated with linear wave propagation is comparable with the nonlinear cascade time. Broadly speaking, these models can be grouped into those that include SDDA in the critical balance condition and those that do not, resulting in different predictions for the scaling properties of turbulence spectra, SDDA and turbulence anisotropy. Although several numerical simulations to date have shown strong evidence for the existence of a SDDA, consistent with theoretical predictions for the energy spectrum, direct observational evidence of SDDA in the solar wind inertial range has been largely inconclusive. In this talk I present a brief overview of Boldyrev's SDDA phenomenology, its verification in numerical simulations as well as previous attempts to detect SDDA in solar wind observations. I will also present new results from a large statistical analysis of WIND measurements that show observational evidence of a power law scaling of the alignment angle between velocity and magnetic fluctuations, consistent with the observed scaling of the energy spectrum and Boldyrev's SDDA phenomenology.