<DOC>
<DOCNO>
151
</DOCNO>
<TITLE>
the generation of noise by isotropic turbulence .
</TITLE>
<AUTHOR>
proudman,j.
</AUTHOR>
<BIBLIO>
proc.roy.s.a 214,1952,119.
</BIBLIO>
<TEXT>
a finite region, with fixed boundaries, of an
infinite expanse of compressible fluid is in
turbulent motion .  this motion generates noise
and radiates it into the surrounding fluid .
the acoustic properties of the system are studied
in the special case in which the turbulent
region consists of decaying isotropic turbulence .
it is assumed that the reynolds number
of the turbulence is large, and that the mach number is small .
  the noise appears to be generated mainly
by those eddies of the turbulence whose
contribution to the rate of dissipation of kinetic
energy by viscosity is negligible .
  it is shown that the intensity of sound at large
distances from the turbulence is the same
as that due to a volume distribution of simple acoustic
sources occupying the turbulent region .
in this analogy, the whole fluid is to be regarded
as a stationary and uniform acoustic
medium .  the local value of the acoustic power output
p per mass of turbulent fluid is given
approximately by the formula
where a is a numerical constant, u is the
mean-square velocity fluctuation, is the time, and
c is the velocity of sound in the fluid .  the
constant a is expressed in terms of the well-known
velocity correlation function f(r) by
assuming the joint probability distribution of the
turbulent velocities and their first two
time-derivatives at two points in space to be
gaussian .  the numerical value is
then obtained by substituting the form of f(r)
corresponding to heisenberg's theoretical
spectrum of isotropic turbulence .
  it is found that the effects of decay make
only a small contribution to the value of a, and
that the order of magnitude of a is not changed
when widely differing forms of the function
f(r) are used .
</TEXT>
</DOC>
