Correlations involving pressure fluctuations in homogeneous turbulence Page: 3 of 62
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NACA TN 3116
also intimately connected with the onset of cavitation in turbulent flow
The pressure-gradient fluctuation, in connection with diffusion in
isotropic turbulence, was first considered by Taylor (ref. 1). He postu-
2 2 2
lated that 1 is of the order u21 independent of Reynolds
number of turbulence. Heisenberg (ref. 2) later derived, from detailed
spectral considerations, an expression for Pplx2 as follows:
(/)p2 P~ u2lu xl)2 where R = u2/v ul/xl)2 is the
Reynolds number of turbulence and the symbols are defined in the symbol
Obukhov (ref. 3) derived an expression for the correlation of pres-
sure with itself for distances between two points whose spacing is within
Kolmogoroff's "inertial subrange." Batchelor (ref. 4) and Limber (ref. 5)
have considered the pressure-pressure and pressure-and-two-velocity-
component correlations in isotropic turbulence. Chandrasekhar (ref. 6)
has considered these correlations for the isotropic turbulence in
magnetohydrodynamics. All these correlations can be expressed in terms
of the correlations involving two components of velocity at one point
and two components at another point. These investigators have from the
very beginning assumed a simple relation between the fourth-order and
the second-order correlations. In order to compare the primary result
with experiment it is necessary to have the results in terms of the
Next to the simplest case of istropic turbulence is homogeneous
axisymmetric turbulence, in which all statistical properties are symmetric
about a particular axis, instead of being spherically symmetric as in the
case of isotropic turbulence. This introduces one new element: The
energies in different components of the velocity are not the same and
there is a transfer of energy from one component of velocity to another.
In the present paper an overbar indicates mean value or statistical
average and an underbar indicates a vector quantity.
2The main results were derived before the publication of refer-
ences 4 to 6, but publication was delayed until the completion of the
experiments reported here.
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Uberoi, Mahinder S. Correlations involving pressure fluctuations in homogeneous turbulence, report, January 1954; (digital.library.unt.edu/ark:/67531/metadc57051/m1/3/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.