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It is shown that the correlation of fluctuating static pressure (in an incompressible and homogeneous turbulence) with any fluctuating quantity 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 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 (r.m.s.) pressure and pressure gradients are computed from second-order correlation for a range of turbulence Reynolds Numbers. Since the pressure gradient is related to diffusion of marked particles from a source, the computed pressure gradient level is compared with that calculated from a set of diffusion measurements.
Mahinder S. Uberoi (1953) studied this question.