  It is shown that distributed chaos with spontaneously broken time
translational symmetry (homogeneity) has a stretched exponential frequency
spectrum $E(f) \propto \exp-(f/f_0)^{1/2}$. Good agreement has been established
with a laboratory experimental data obtained at large values of Rayleigh number
$Ra \sim 3\cdot 10^{14}$ in thermal convection. Applications to geophysical
fluid dynamics (temperature dynamics for large cities, the North Atlantic
Oscillation index and the Pacific/North American pattern) have been considered.
