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 , \langle \rho \rangle .
When \langle \rho \rangle is in the range ( 1 – 5 ) \times 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 \langle p \rangle is independent of \langle \rho \rangle and just a little above the minimum value .
For a constant heating rate of 0.015 { erg } { g } ^ { -1 } { s } ^ { -1 } , the mean pressure is around 24 \times 10 ^ { -14 } { dyn } ( corresponding to p / k _ { B } \approx 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 are obtained , the resulting dissipation rates rates are comparable to the thermal energy input rate .
The resulting mean pressures are then about 30 \times 10 ^ { -14 } { dyn } , corresponding to p / k _ { B } \approx 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 .