Simulation of turbulent acoustic sources in the Sun

Oscillatory behavior is one of the basic properties of the solar surface. Stochastic wave excitation in the turbulent convective medium and frequent interference of acoustic wavefronts make the problem of understanding of the mechanism of solar oscillations very complicated. In observational data individual wave excitation events overlap with other wave events. Nevertheless, individual impulsive events generating acoustic waves have been detected by the Vacuum Tower Telescope (Sacramento Peak Observatory). According to data analysis and numerical simulations, the source of solar acoustic waves with a typical period of 5 min is located in the turbulent convection layer ∼ 200 km below the solar surface (Goode et al. 1992). Such impulsive events usually occur in intergranular lanes of the granulation pattern, and are associated with local strong cooling of fluid elements (Rimmele et al. 1995). At the present time there is no clear explanation of the mechanism of acoustic wave sources on the Sun. In turbulence theory, the wave excitation process was initially studied by Lighthill (1952) for acoustic wave’s generated by air flow. According to the theory, a mechanism for the transfer of the flow kinetic energy to acoustic energy can be caused by short-time deformation of fluid elements by shear flows (Lighthill 1954). The importance of turbulence as a source of wave generation on the Sun was confirmed by numerical simulations. In particular, the numerical results of Stein & Nordlund (2001) supported the observations that strong acoustic sources are located near the solar surface. The simulations also supported the observation that these sources are located at the intergranular lanes or in their vicinity, where wave excitation is related to occasional, high-pressure fluctuations associated with the initiation of turbulent downdrafts and, sometimes, with intergranular lane formation. These are relatively small-scale events compared to the granular structure. Current numerical simulations cannot resolve all of the turbulence scales in the solar conditions. As accurate sub-grid scale modeling of turbulence is therefore important when the events of interest are part of the cascade of turbulence scales. In particular, Jacoutot et al. (2008a) studied several turbulence models and found that the best agreement of the synthetic (simulated) oscillation power spectrum with observational data is given by a dynamic formulation of the Smagorinsky model (Germano et al. 1991; Moin et al. 1991). The problem of resolving small-scale turbulent eddies is also evident in our observing capabilities. Observations were able to resolve relatively large, ∼ 3 Mm in diameter, vortex flows in the photosphere (Brandt et al. 1988). Then, evidence for vortex motions was found from an example of two bright points rotating around each other (Wang et al. 1995). Other observations of vortices showed a connection of vortex motions to strong downflows (Pötzi & Brandt 2005). Recent observations were able to detect a number