Turbulence and distributed chaos with spontaneously broken symmetry
  It is shown that in turbulent flows the distributed chaos with spontaneously
broken translational space symmetry (homogeneity) has a stretched exponential
spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. Good agreement has
been established between the theory and the data of direct numerical
simulations of isotropic homogeneous turbulence (energy dissipation rate
field), of a channel flow (velocity field), of a fully developed boundary layer
flow (velocity field), and the experimental data at the plasma edges of
different fusion devices (stellarators and tokamaks). An astrophysical
application to the large-scale galaxies distribution has been briefly discussed
and good agreement with the data of recent Sloan Digital Sky Survey SDSS-III
has been established.
