Alfvén gravity waves in viscous solar plasma: Effect of the background flow

We study the Propagation and damping properties of Alfvén gravity waves in the presence of the vertical magnetic field in the viscous solar plasma under influence of the background flow by deriving a fourth order dispersion relation in terms of the Doppler shifted frequency. We derive the dispersion relation under WKB and Boussinesq approximation. We study the damping of Alfvén gravity waves for the wave frequencies less than and greater than the Brunt-Väisälä frequency. We find that the Brunt-Väisälä frequency divides the frequency ranges where the weakly or strongly damped oscillations occur. The background flow exhibits a strong effect on weakly damped oscillations and a weak effect on the strongly damped oscillations. We also notice that the damping of both the strong and weakly damped oscillations depend on the Brunt-Väisälä frequency and wave number. The effect of the background flow is also being governed by the Brunt-Väisälä frequency and wave number. We also study the properties of gravity wave mode after filtering the Alfvén wave mode by minimizing the magnetic field and noticed that the background flow shows a very strong effect on the gravity wave mode.