  We employ a generalization of the She & Leveque model to study velocity
scaling relations based on our simulations of thermal instability--induced
turbulence. Being a by-product of the interstellar phase transition, such
multiphase turbulence tends to be more intermittent than compressible
isothermal turbulence. Due to radiative cooling, which promotes nonlinear
instabilities in supersonic flows, the Hausdorff dimension of the most singular
dissipative structures, D, can be as high as 2.3, while in supersonic
isothermal turbulence D is limited by shock dissipation to D < 2. We also show
that single-phase velocity statistics carry only incomplete information on the
turbulent cascade in a multiphase medium. We briefly discuss the possible
implications of these results on the hierarchical structure of molecular clouds
and on star formation.
