Hamiltonian fluid dynamics and distributed chaos

It is shown that distributed chaos with spontaneously broken time translational symmetry (homogeneity) has a stretched exponential frequency spectrum $E(f)\propto \exp -(f\mathrm{/}{f}_0{)}^{1\mathrm{/}2}$. 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.