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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(4):408-422; doi:10.1093/qjmam/5.4.408
© 1952 by Oxford University Press
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THE DECAY OF SHOCK WAVES

W. CHESTER

( Dept. of Mathematics, The University Bristol )

The interaction of the shock and rarefaction waves produced in a gas-filled tube, closed at one end by a moving piston, is discussed. The piston is moved impulsively to produce two waves of rarefaction separated by a shock. The decay of the latter, resulting from its interaction with the two plane waves, is described on the basis of an approximate treatment in which all terms of the third order in the shock strength are ignored. In particular, entropy variations are disregarded. It is shown that the strength of the shock decays inversely as the time.

The application of the results to the more general problem, in which the piston experiences a series of impulsive changes in velocity in such a way that shock waves and centred rarefaction waves are formed alternately, is discussed.

Finally the analogous problem involving the two-dimensional steady flow of a gas along an indented wall is considered.


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