Abstract : Stars drive the evolution of the universe but their formation remains a theoretical challenge. One central issue in the evolution of the gas towards star formation is the dissipation of its turbulent energy at large, including the contributions of magnetic fields and cosmic-rays. A fundamental property of turbulence is its intermittency : dissipation occurs in bursts, unevenly distributed in space and time. The origin of the intermittency of turbulence is far from being understood on theoretical grounds. While it is studied in laboratory flows, its properties in compressible and non-ideal magnetized turbulence are still elusive.
Numerical simulations dedicated to turbulent dissipation in interstellar turbulence have been performed to provide observable statistical properties of intermittency. Several signatures of turbulent intermittency in the galactic interstellar medium will be presented, including those found in the all-sky polarization of the dust thermal emission of the Planck survey, and in the large abundances of some specific molecules with highly endoenergic formation routes observed with Herschel. One of these molecules has recently been discovered with the ALMA interferometer in starburst galaxies at high redshift. The absorption and emission lines unveil a hidden facet of the gravitational and turbulent energy trails in these sources.