<DOC>
<DOCNO>
132
</DOCNO>
<TITLE>
viscosity effects in sound waves of finite amplitude:
in survey in mechanics .
</TITLE>
<AUTHOR>
lighthill,m.j.
</AUTHOR>
<BIBLIO>
ed. by g.k.batchelor and r.m.davies.  c.u.p. 1956.
</BIBLIO>
<TEXT>
  this article has as its subject /the conflicting influence on
sound propagation of convection on the one hand, and of diffusion
and relaxation on the other/, whose importance in the determination
of the structure of shock waves was first appreciated clearly
by sir geoffrey taylor .  as an essential introduction to the main
topics, author gives an exceptionally clear and valuable account
of the physical mechanisms of viscosity, thermal conductivity, and
other diffusion effects, including relaxation .  the classical theory
of shock-wave formation is then discussed, and some extensions
are made .
  the remainder of the article is based on the demonstration that
the nonlinear equation for plane progressive sound waves, in which
convection and diffusion are taken into account to a first approximation,
can be transformed into burgers's equation, the general
solution of which was given by hopf and cole .  this approach, in
which all flows are continuous (they become discontinuous at
shock waves in the limit as viscosity, etc., tend to zero), allows
the author to re-derive and extend whitham's theory of the formation
and decay of weak plane shock waves, and to derive many
new results, such as the velocity distributions during the union
of two shock waves and during the formation of a shock wave .
the application of the same idea to non-plane shock waves is
also discussed, but more briefly,. in these cases, burgers's equation
is not quite such a good approximation as before .
  the article concludes with sections on sound waves whose
reynolds numbers based on the length scale of the flow and the
velocity amplitude are comparable with unity, and on the effects
of relaxation on the properties of shock waves .  the whole is
much more than a survey, and represents a very substantial advance
in the theory of sound waves .  it is the finest possible
tribute to sir geoffrey taylor that he should be able to inspire
articles such as this and the others in this volume .
</TEXT>
</DOC>
