Pressure statistics for locally isotropic turbulence

The pressure structure function $D_P\mathrm{}\left(r\right)\mathrm{}$ and pressure-gradient correlation $A_{\mathrm{ij}}(r\to )$ are related to components of the fourth-order velocity structure function $D_{\mathrm{ijkl}}(r\to )$ on the basis of the Navier-Stokes equation, incompressibility, local homogeneity, and local isotropy. Data from a wind tunnel, as well as numerical simulation, are used to calculate $D_P\mathrm{}\left(r\right)\mathrm{}$ and thereby show that greater Reynolds numbers are needed to observe an inertial range in $D_P\mathrm{}\left(r\right)\mathrm{}$ than in $D_{\mathrm{ijkl}}(r\to ).\mathrm{}$ A previous additional supposition relates $D_P\mathrm{}\left(r\right)\mathrm{}$ and $A_{\mathrm{ij}}(r\to )$ to the single component $D_{1111}\mathrm{}\left(r\right).$ This additional supposition is shown to be inaccurate for calculation of $D_P\mathrm{}\left(r\right)\mathrm{}$ and $A_{\mathrm{ij}}(r\to ).\mathrm{}$