to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in [*stronger loop fields*]{} and lead to [*larger heating rates*]{} than in weak field regions.
author:
- 'A.F. Rappazzo, M. Velli'
- 'G. Einaudi'
- 'R.B. Dahlburg'
title: Nonlinear Dynamics of the Parker Scenario for Coronal Heating
---

INTRODUCTION
============

In a previous letter [@rap07] we described simulations, within the framework of RMHD in cartesian geometry, aimed at solving the Parker field-line tangling (coronal heating) problem [@park72; @park88]. We also developed a phenomenological model for nonlinear interactions, taking into account the inertial photospheric line-tying effect, which explained how the average coronal heating rate would depend on the only free parameter present in the simulations, namely the ratio of the coronal loop Alfvén crossing time and the photospheric eddy turnover time. This paper is devoted to a more detailed discussion of the numerical simulations and of the relationship between this work, the original Parker conjecture, and the nanoflare scenario of coronal heating.

Parker’s book [@park94] is devoted to an examination of the basic theorem of magnetostatics, namely that the lowest available energy state of a magnetic field in an infinitely conducting fluid 