## 1. IntroductionRecently in solar physics a certain interest has arisen to the problem of interaction of waves and steady flows. In particular, flows can affect MHD waves trapped by magnetic flux tubes, modifying dispersion relations and changing wave cut-offs (Nakariakov & Roberts 1995). Also, it was shown (Joarder et al. 1997) that in the photosphere and below, observationally registered down-flows can cause negative energy wave effects, leading to instability and over-stability of the waves due to their interaction with the flows. In Nakariakov et al. (1998), it was found that even very weak flows, as long as they had sufficiently sharp gradients, can dramatically affect propagation of the waves, causing enhanced coupling of different wave modes. Thus, it is believed that the wave-flow interactions play a very important role in the dynamics of the solar plasma. The Sun exhibits global oscillations which are influenced by a
turbulent flow in the convection zone. The first evidence of these
oscillations was provided by Leighton et al. (1962) who measured the
Doppler shifts of photospheric spectral lines. Subsequently, it was
proposed by Ulrich (1970) that acoustic waves were the cause of the
Doppler shifts. As pressure provides the restoring force for these
oscillations, they are called Although recent investigations prove that new solar models closely
describe the Sun, there are still significant discrepancies between
the predictions and the observations of the The influence of convection on solar oscillations was discussed by
several authors. In particular, Brown (1984), while considering
vertical velocity perturbations, suggested that such perturbations
cause a frequency decrease of sufficient magnitude to produce an
observable effect. Lavely & Ritzwoller (1992) used perturbation
theory to investigate the effects of steady-state convection on the
This paper is organized as follows. The next section presents linear equations which describe the interaction between the flow and the acoustic waves. Sect. 3 presents the random dispersion relation which is solved numerically for the case of a space-dependent random flow as well as for a time-dependent flow. Sect. 4 is devoted to numerical simulations of linear hydrodynamic equations. The paper is concluded by a short summary. © European Southern Observatory (ESO) 2000 Online publication: July 7, 2000 |