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The D’yakov work which deals with a shock that undergoes a slight disturbance is re−examined. Under a linear analysis the growth of perturbations is examined and this produces inequality restrictions for the shock to be stable. It is found that the shock is unstable for j2(dv/dp)H 〈−1 and j2(dv/dp)H〉 1 + 2M, where M is the Mach number of the shock with respect to the material behind, and −j2 is the slope of the Rayleigh line. These inequalities agree with those of D’yakov. It is also shown that these results are exactly the same as those derived by Erpenbeck by a different analysis. Some properties of general Hugoniot curves are also presented. It is demonstrated that the restriction to M<1, by itself, does not restrict the range of values for the slope of the Hugoniot curve.

No abstract

A new argument is presented that yields the following criterion for plane shocks to be stable: -lV) is the slope of the Rayleigh line, and (dv/dp)# is the slope of the Hugoniot curve in the pressure-volume plane. The lower limit is well known and the consequences of its violation are well understood; however, no such degree of understanding has yet been achieved for the upper limit. It seems likely that it bears an important relation to detonation phenomena.We have recently re-examined some of the theoretical results on the stability of plane shocks: This work included a careful check by one of us (G.W.S.) of an analysis by D'yakov. 1 In attempting to understand the conclusions we conceived a new approach to the problem that leads to a different stability limit than has previously been derived.In the analysis of D'yakov, and also that of Erpenbeck 2 whose mathematical technique was different, a plane steady shock is perturbed and the growth with time of the perturbation quantities are examined via the one-dimensional flow equations in linearized form. The stability limits can be summarized as -l