Correlations involving pressure fluctuations in homogeneous turbulence Page: 2 of 62
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TECH LIBRARY KAFB, NM
NATIONAL ADVISORY COMMITTEE FOR AERONAUTIC;0065991
TECHNICAL NOTE 3116
CORRELATIONS INVOLVING PRESSURE FLUCTUATIONS
IN HOMOGENEOUS TURBULENCE
By Mahinder S. Uberoi
It is shown that the correlation of fluctuating static pressure (in
an incompressible and homogeneous turbulence) with any fluctuating quan-
tity in the flow field can be expressed in terms of the correlation of
the same quantity with two or more components of the velocity.
The correlations of pressure with itself and of pressure with two
velocity components are investigated in detail for the case of isotropic
turbulence. These correlations can be expressed in terms of correlations
involving two velocity components at a point and two velocity components
at another point. A postulated relation between the fourth-order and
second-order correlations is investigated. This relation is satisfied,
for example, if the joint probability density of the four components of
velocity is Gaussian. The consequences of this relation are compared
with the measurements of the fourth-order correlations.
The root-mean-square pressure and pressure gradients are computed
from second-order correlation for a range of turbulence Reynolds num-
bers. Since the pressure gradient is related to diffusion of marked
particles from a source, the computed pressure-gradient level is com-
pared with that calculated from a set of diffusion measurements.
The triple correlation equation and plausible hypotheses relating
higher order correlations with second-order correlation are examined for
the possibility of getting a determinant set of equations for isotropic
Although in isotropic turbulence the dynamical (correlation) equa-
tion does not contain any pressure correlations, the correlation of pres-
sure with itself is of interest in turbulent diffusion and in the study
of sound generation by turbulence (for very low Mach numbers of turbulence
velocities when there is little effect of sound on the turbulent field,
that is, only a slight amount of energy is drained away from the turbulent
energy in the form of sound waves). The static pressure fluctuations are
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Uberoi, Mahinder S. Correlations involving pressure fluctuations in homogeneous turbulence, report, January 1954; (digital.library.unt.edu/ark:/67531/metadc57051/m1/2/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.