Wavelength limits on isobaricity of perturbations in a thermally unstable radiatively cooling medium

Nonlinear evolution of one-dimensional planar perturbations in an optically thin, radiatively cooling medium in the long-wavelength limit is studied n umerically. The accepted cooling function generates, in thermal equilibrium , a bistable equation of state P(rho). The unperturbed state is taken close to the upper (low-density) unstable state with infinite compressibility (d P/d rho = 0). The evolution is shown to proceed in three different stages. At the first stage, pressure and density set in the equilibrium equation of state, and velocity profile steepens gradually, as in the case of pressure -free flows. At the second stage, those regions of the flow where anomalous pressure (i.e., with negative compressibility) holds create a velocity pro file sharper than in the pressure-free case, which in turn results in forma tion of a very narrow (short-wavelength) region where gas separates the equ ilibrium equation of state and pressure equilibrium sets in rapidly. At thi s stage, the variation in pressure between the narrow dense region and the extended environment does not exceed more than 0.01 of the unperturbed valu e. At the third stage, gas in the short-wavelength region reaches the secon d (high-density) stable state, and pressure balance establishes through the flow, with pressure equal to the one in the unperturbed state. In external (long-wavelength) regions, gas forms slow isobaric inflow toward the short -wavelength layer. The duration of these stages decreases when the ratio of the acoustic time to the radiative cooling time increases. The limits in w hich nonlinear evolution of thermally unstable long-wavelength perturbation s develops in isobaric regime are obtained. (C) 1999 American Institute of Physics. [S1070-664X(99)01401-9].