Pressure statistics for locally isotropic turbulence

The pressure structure function D-p(r) and pressure-gradient correlation A(ij)((r) over right arrow) are related to components of the fourth-order velocity structure function D-ijkl((r) over right arrow) 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(r) and thereby show that greater Reynolds numbers are needed to observe an inertial range in D-p(r) than in D-ijkl((r) over right arrow). A previous additional supposition relates D-p(r) and A(ij)((r) over right arrow) to the single component D-llll(r). This additional supposition is shown to be inaccurate for calculation of D-p(r) and A(ij)((r) over right arrow).