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136 3. Further applications

directions, so any disturbance generated in the gas is assumed to propagate (and possibly
change) only in is time. The speed of the gas is and its pressure, density and
temperature are and respectively.
First, we suppose that the gas in its stationary undisturbed state is described
by

all constant. The gas is now disturbed, thereby producing a weak pressure wave (often
called an acoustic wave, although this is usually treated with temperature fixed); the size
of the initiating disturbance will be measured by the parameter We introduce
the sound speed, of the gas in its undisturbed state, defined by

and then we move to non-dimensional variables (without the primes) by writing

we let a typical or appropriate length scale (e.g. an average wave length) be and also
define

The governing equations, (3.60)–(3.63), therefore become

where the Reynolds Number is and the Prandtl Number is
with (Note that we have elected to define the speed in the defi-
nition of as which is proportional to the scale of the speed generated by the
disturbance; a suitable choice of is a crucial step in ensuring that we obtain the
limit of interest.)