  It is shown that correlation function of the mean wind velocity in a
turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits
exponential decay with a very long correlation time, while corresponding
largest Lyapunov exponent is certainly positive. These results together with
the reconstructed phase portrait indicate presence of a chaotic component in
the examined mean wind. Telegraph approximation is also used to study relative
contribution of the chaotic and stochastic components to the mean wind
fluctuations and an equilibrium between these components has been studied.
Since solar activity is based on the thermal convection processes, it is
reasoned that the observed solar activity long-term correlations can be an
imprint of the mean wind chaotic properties. In particular, correlation
function of the daily sunspots number exhibits exponential decay with a very
long correlation time and corresponding largest Lyapunov exponent is certainly
positive, also relative contribution of the chaotic and stochastic components
follows the same pattern as for the convection mean wind.
