## 4. Dispersion relation for the turbulent () plasmaThe solar plasma below the visible layers is a dynamic environment,
supporting convection which reveals itself principally on two spatial
scales of motion: a large scale supergranulation with horizontal scale
of km and flows of 0.1-0.4 km/s and
much smaller scale granulation with horizontal scale of
km and flows of 1-3 km/s (Simon et
al. 1991). Temporal scales associated with these motions range from 30
minutes for granule overturn times to weeks for giant cells. Such
dynamic medium is expected to influence the We consider a model in which weak turbulent field is settled in the convection zone. This assumption is valid since the turbulence reveals speeds km/s which are small in comparison to the sound speed km/s. Consequently, we can use the following expansion: where and represent coherent and random fields, respectively. The symbol denotes ensemble averaging (e.g., Ishimaru 1978). Substituting this expansion into linearized Eqs. (2)-(6) after lengthy algebra in which the binary collision approximation (Howe 1971) has been used, we obtain the dispersion relation The functions and , , are solutions of Eq. (10). The formulae which determine the right hand side of this equation are presented in Appendix A. Here, denotes the Fourier transform operator evaluated at and . From dispersion relation (21) it follows that the dependence of the
cyclic frequency on the wavevector
© European Southern Observatory (ESO) 2000 Online publication: August 17, 2000 |