Thermal instability in shearing and periodic turbulence

The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, [rho]. When [rho] is in the range (1-5); 10(-24) g cm(-3), the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10(4) K, respectively. However, in all cases the resulting average pressure [p] is independent of [rho] and just a little above the minimum value. For a constant heating rate of 0.015 ergs g(-1) s(-1), the mean pressure is around 24 x 10(-14) dyn (corresponding to p/ k(B) approximate to 1750 K cm(-3)). Cool patches tend to coalesce into bigger ones. In all cases investigated, there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km s(-1) are obtained, the resulting dissipation rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10(-14) dyn, corresponding to p/k(B) approximate to 2170 K cm(-3). This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability.