The pressure structure function DP(r) and pressure-gradient correlation Aᵢⱼ(r→) are related to components of the fourth-order velocity structure function Dᵢⱼₖₗ(r→) 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 DP(r) and thereby show that greater Reynolds numbers are needed to observe an inertial range in DP(r) than in Dᵢⱼₖₗ(r→). A previous additional supposition relates DP(r) and Aᵢⱼ(r→) to the single component D₁₁₁₁(r). This additional supposition is shown to be inaccurate for calculation of DP(r) and Aᵢⱼ(r→).
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Hill et al. (1997) studied this question.
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