Lyapunov exponents for solar surface convection

We have carried out detailed 2D numerical radiation hydrodynamics calculations, specifically designed to model time-dependent, compressible convection in the surface layers of the Sun. These simulations, which take into account a realistic equation of state and use an elaborate scheme to describe multi-dimensional, non-local, frequency-dependent radiative transfer, allow a direct comparison with observed photometric and spectroscopic properties of solar granulation. Their purpose is to enhance our understanding of the dynamics and thermal structure of convective stellar atmospheres, and to investigate the generation of acoustic energy by turbulent convection. Here, we briefly present some of the main properties of our solar convection models. In particular, we demonstrate the chaotic behaviour of solar surface convection, estimating the magnitude of the two largest Lyapunov exponents, λ1 and λ2, by analysing the time evolution of three simulations with slightly different initial conditions. We find that both λ1 and λ2 are positive and of similar magnitude, as expected for a chaotic system of high dimension. The corresponding characteristic time scale λ1−1 of approximately 320 s is comparable to the convective turnover time.