5. Discussion and conclusions
The resonant dissipation of Alfvén waves in coronal loops is a promising explanation for the high temperatures in the solar corona. We have studied the resonant heating mechanism in the framework of nonlinear resistive MHD and focussed on the dynamics of the resonant layers. The simulations presented in this paper clearly demonstrate that the dynamics of the shear flow in the resonant layers is very nonlinear for typical coronal loop parameter values. The nonlinearity manifests itself by the excitation of `overtones' of the incident waves. For typical coronal parameter values this nonlinear mode coupling is quite substantial and, hence, nonlinear effects need to be taken into account when deriving quantitative results on the efficiency of resonant absorption as a coronal heating mechanism.
From the numerical simulations discussed here one can conclude that the heating rate due to resonant dissipation is lower than the heating rate predicted by linear MHD simulations, in spite of the fact that the nonlinear mode coupling yields an energy cascade to smaller length scales. This qualitative statement is quantified by Poedts et al. 1996, who calculated the actual Ohmic dissipation rate for a linear MHD simulation that is continued in nonlinear MHD.
It is important to notice that for conclusive statements about the role of wave heating in the solar corona the relatively simple model used in the present paper should be improved by including, e.g., density variation, effects of line-tying, thermal conduction, etc. Also, more and better observations are required of the internal structure of the coronal loops, both in the radial and in the longitudinal direction. The radial structure is most important for heating by resonant absorption because it is the stratification in the radial direction which determines the time scales and the localisation of the heat deposition. Moreover, information is required on the waves that might cause these changes, i.e., on the power spectrum of the waves that excite the coronal loops both side-ways and at the footpoints.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998