Poynting's theorem in magnetic turbulence

Abstract

Poynting's theorem is used to obtain an expression for the turbulent power-spectral density as function of frequency and wavenumber in low-frequency magnetic turbulence. No reference is made to Elsasser variables as is usually done in magnetohydrodynamic turbulence mixing mechanical and electromagnetic turbulence. We rather stay with an implicit form of the mechanical part of turbulence as suggested by electromagnetic theory in arbitrary media. All of mechanics and flows is included into a turbulent response function which by appropriate observations can be determined from knowledge of the turbulent fluctuation spectra. This approach is not guided by the wish of developing a complete theory of turbulence. It aims on the identification of the response function from observations as input into a theory which afterwards attempts its interpretation. Combination of both the magnetic and electric power spectral densities leads to a representation of the turbulent response function, i.e. the turbulent conductivity spectrum $\sigma_{\omega k}$ as function of frequency $\omega$ and wavenumber $k$. {It is given as the ratio of magnetic to electric power spectral densities in frequency space. This knowledge allows for formally writing down a turbulent dispersion relation. Power law inertial range spectra result in a power law turbulent conductivity spectrum. These can be compared with observations in the solar wind. Keywords: MHD turbulence, turbulent dispersion relation, turbulent response function, solar wind turbulence