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The main observational evidence for turbulence in the interstellar medium(ISM) and molecular clouds is the power-law energy spectrum for velocityfluctuations, E(k) \propto k^{\alpha}. The Kolmogorov scaling exponent,\alpha=-5/3, is typical. At the same time, the observed probabilitydistribution function (PDF) of gas densities in both the ISM as well as inmolecular clouds is a log-normal distribution, which is similar to the initialmass function (IMF) that describes the distribution of stellar masses. Weexamine the density and velocity structure of interstellar gas traversed bycurved shock waves in the kinematic limit. We demonstrate mathematically thatjust a few passages of curved shock waves generically produces a log-normaldensity PDF. This explains the ubiquity of the log-normal PDF in many differentnumerical simulations. We also show that subsequent interaction with aspherical blast wave generates a power-law density distribution at highdensities, qualitatively similar to the Salpeter power-law for the IMF.Finally, we show that a focused shock produces a downstream flow with energyspectrum exponent \alpha=-2. Subsequent shock passages reduce this slope,achieving \alpha \approx -5/3 after a few passages. Subsequent dissipation ofenergy piled up at the small scales will act to maintain the spectrum very nearto the Kolomogorov value. Therefore, fully-developed turbulence may not berequired to explain the observed energy spectrum and density PDF. We argue thatthe self-similar spherical blast wave arising from expanding HII regions orstellar winds from massive stars may ultimately be responsible for creating thehigh mass, power-law, tail in the IMF.

Shock generated vorticity in the interstellar medium and the origin of the stellar initial mass function