Turbulent dissipation in the interstellar medium: The coexistence of forced and decaying regimes and implications for galaxy formation and evolution

We discuss the dissipation of turbulent kinetic energy E-k in the global in terstellar medium (ISM) by means of two-dimensional, MHD, nonisothermal sim ulations in the presence of model radiative heating and cooling. We argue t hat dissipation in two dimensions is representative of that in three dimens ions as long as it is dominated by shocks rather than by a turbulent cascad e. Contrary to previous treatments of dissipation in the ISM, this work con siders realistic, stellar-like forcing : energy is injected at a few isolat ed sites in space, over relatively small scales, and over short time period s. This leads to the coexistence of forced and decaying regimes in the same flow, to a net propagation of turbulent kinetic energy from the injection sites to the decaying regions, and to different characteristic dissipation rates and times in the forced sites and in the global flow. We find that th e ISM-like flow dissipates its turbulent energy rapidly. In simulations wit h forcing, the input parameters are the radius l(f) of the forcing region, the total kinetic energy each source deposits into the flow, and the rate o f formation of those regions, (Sigma )over dot(OB). The global dissipation time t(d) depends mainly on l(f). We find that for most of our simulations t(d) is well described by a combination of parameters of the forcing and gl obal parameters of the flow: t(d) approximate to u(rms)(2)/((epsilon )over dto(k) f), where u(rms) is the rms velocity dispersion, (epsilon )over dot( k) is the specific power of each forcing region, and f is the filling facto r of all these regions. In terms of measurable properties of the ISM, t(d) greater than or similar to < Sigma (g)>u(rms)(2)/(e(k) (Sigma )over dot(OB) ), where is the average gas surface density; for the solar neighborhood, yr . The global dissipation time is consistently smaller than the crossing tim e of the largest energy-containing scales, suggesting that the local dissip ation time near the sources must be significantly smaller than what would b e estimated from large-scale quantities alone. In decaying simulations, we fund that the kinetic energy decreases with time as E-k(t) proportional to t(-alpha) where alpha approximate to 0.8-0.9. This result can be translated into a decay with distance l when applied to the mixed forced-plus-decayin g case, giving Ek proportional to l(-2 alpha/(2-alpha)) at large distances from the sources. Our results, if applicable in the direction perpendicular to galactic disks, support models of galaxy evolution in which stellar ene rgy injection provides significant support for the gas disk thickness but d o not support models in which this energy injection is supposed to reheat a n intrahalo medium at distances of up to 10-20 times the optical galaxy siz e, as the dissipation occurs on distances comparable to the disk height. Ho wever, this conclusion is not definitive until the effects of stratificatio n on our results are tested.