On the Instability of Decelerating Shock Waves

Details On the Instability of Decelerating Shock Waves On the Instability of Decelerating Shock Waves

Feb 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992pthph..87..347n&link_type=abstract

Progress of Theoretical Physics, Vol. 87, No. 2, pp. 347-365

Physics

15

Scientific paper

We examine the decelerating shock instability (DSI) with a linear perturbation theory. We also investigate the effect of the self-gravity on the instability of a decelerating shocked layer. We find that the characteristics of the DSI can be obtained with a thin layer approximation and that the DSI is caused by the combination of the fluctuation of column density induced by the rippling of the shocked layer and the deceleration of the layer as a whole. There is a typical wavenumber kS(equiv 2 beta(1/2) x (1 - beta)(-1/2}|dot{V}S0|/cS({2)) ) in the dispersion relation of the DSI, where beta is the pressure ratio of the trailing side to the leading side of the shocked layer, dot{V}S0 is the deceleration of the shock wave and cS is the sound speed. The thermal pressure in the layer has a stabilizing effect especially at k gtrsim kmax. When the self-gravity plays an important role, the dispersion relation is found to be characterized by the parameter alpha equiv kS/kG, where kG equiv 2pi Gsigma0/cS(2) , G being the gravitational constant and sigma0 the column density of the shocked layer. In the case alpha > 1, the layer is unstable only to the DSI. If alpha < 1, there are two types of instabilities. For the wavenumber k < (kG - kS)/g(alpha, beta), where g(alpha, beta) is a factor of the order of unity, the layer is gravitationally unstable and for (kG - kS)/g(alpha, beta) < k < (kG + kS)/g(alpha, beta), the layer is overstable and the instability is the DSI mode. This dispersion relations may be related to the hierarchical structure of clumps and cores observed in the star forming regions around H II regions.

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