Linear and Nonlinear Waves in Shock-Bounded Slabs

Details Linear and Nonlinear Waves in Shock-Bounded Slabs Linear and Nonlinear Waves in Shock-Bounded Slabs

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995nyasa.773...70v&link_type=abstract

Waves in Astrophysics, vol. Volume 773, p. 70-79

Astronomy and Astrophysics

Astrophysics

2

Nonlinear Equations, Linear Equations, Shock Waves, Slabs, Computerized Simulation, Equations Of Motion, Boundary Conditions, Thermal Shock, Astrophysics, Interstellar Matter

Scientific paper

The stability of shock waves is a rich topic with a long history. As an abstract problem in hydrodynamics, it has the attractive feature that it is an example of a solvable perturbation problem in strongly nonlinear flows, one that in certain limits can even be tested experimentally. In this paper we review theoretical work on the stability of slabs bounded on at least one side by a strong shock, in the sense that the density contrast across the shock is much larger than one. Where possible we compare these theoretical predictions to computer simulations and experimental work. This is a problem with significant implications for astrophysics for several reasons. First, strong shocks are common in the interstellar medium (ISM), and when radiative cooling is important the density contrast may be very large. Second, the ability of shock waves to generate substructure spontaneously is important for understanding the evolution of structure in the ISM. Third, the late evolution of shock waves, when cooling has become important, affects the efficiency with which the energy associated with bulk flows in the ISM can be converted into turbulent energy and/or radiation. Fourth, the dynamical behavior of shock-bounded slabs determines whether or not gravitationally bound lumps can form inside them. Fifth, and last, the structure of strongly radiating shocks can determine what we see in terms of linewidths and line ratios. Observations are normally interpreted in terms of one-dimensional models, but if there are large postshock flows and density inhomogeneities, these results may be in error. The more interesting, and realistic, problem is one in which the gas is concentrated in a slab with some characteristic thickness, L, and bounded by a shock on at least one face. The other face may be bounded by a shock, by thermal pressure, or by nothing at all (if the shock is decelerating). Here we present the results of several years work on linear and nonlinear instabilities in shock-bounded slabs. For the most part we confine ourselves to quoting general results rather than presenting derivations, which can be found in the cited literature. However, we present many of the details of the averaging procedure, which allows us to find the properties of the nonlinear instabilities. A simpler version of this procedure was used in the initial discovery of the linear instabilities as well.

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