Turbulence Effects at Small Scales

It is most natural to assume that mysterious Small Ionized and Neutral Structures (SINS) in diffuse ISM arise from turbulence. There are two obvious problem with such an explanation, however. First of all, it is generally believed that at the small scales turbulence should be damped. Second, turbulence with Kolmogorov spectrum cannot be the responsible for the SINS. We consider, however, effects, that provide spectral index flatter than the Kol-mogorov one and allow action at very small scales. These are the shocks that arise in high Mach number turbulence and transfer of energy to small scales by instabilities in cosmic rays. Our examples indicate that the origin of SINS may be discovered through systematic studies of astrophysical turbulence. Various observations covered well in this volume indicate the existence of structure in the neutral and ionized ISM on AU spatial scales, causing concern about how well we understand the basics of the ISM physics. In the straightforward interpretation, these clouds should be extremely overdense and and overpres-sured. Evaporation arguments point to very short lifetimes of such clouds, yet the AU-scale structures in the diffuse medium seem quite common. In this volume the reader can find many articles dealing with the observed properties of SINS. Therefore we do not dwell upon this issue. Instead we adopt a broad theoretical approach and ask a question whether turbulence can produce enough activity on small scales to be considered as a potential source of SINS. The attractiveness of turbulence as an origin of SINS is that it can produce a generic universal explanation. Indeed, turbulence is really ubiquitous in astrophysics, including the ISM and circumstellar regions. However, the most popular Kolmogorov turbulence model can not account for SINS. Kolmogorov turbulence has a spectrum of E(k) ∼ k −5/3 , the fluctuations of density at scale k ∼ 1/l arisen from advection by turbulence are (δρ k) 2 ∼ kE(k) ∼ k −2/3 , i.e. they decrease with the scale. SINS, on the contrary, are connected to rather large density contrasts at small scales. This would violate the assumption of Kolmogorov turbulence that it is only weakly compressive at large outer scale. Fortunately, astrophysical turbulence is not limited to the Kolmogorov spectrum. If the spectrum of density fluctuations scales as E(k) ∼ k −n , n < 1, then (δρ k) 2 increases with the decrease of turbulence scale. As we see from the example above, …