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Integral expressions are derived for the mean-square fluctuation pressure, pressure correlation, and certain moments of the pressure correlation within general anisotropic, homogeneous turbulence. Application is made to idealized flow models exhibiting certain anisotropy characteristics similar to those observed in boundary layer turbulence. Pressure fluctuations arising from the turbulence itself and from interaction of the turbulence with a mean flow exhibiting constant shear are compared with the isotropic case. It is found that, in contrast to the completely isotropic case, the anisotropic pressure correlation is negative for some difference coordinate values and exhibits a “tail” which falls off with distance x as x−3 at separations for which the velocity correlations have fallen essentially to zero. It is concluded that in general the principal normalized moments of the pressure correlation will tend to be less than the corresponding velocity correlation moments. For isotropic turbulence this implies that the pressure correlation must fall off with distance faster than the velocity correlation. For the models of anisotropic turbulence treated it is found that departure from isotropy results in lower mean-square pressure fluctuations for a given mean kinetic energy of turbulence.
Robert H. Kraichnan (1956) studied this question.