The 1951 theory of the pressure structure function used the assumption of joint Gaussian velocities to obtain tracta~le results. That theory has recently been replaced by a new theory that does not use this assumption. The relationships between formulas from the two theories are given. It is shown that combining the new theory with the joint Gaussian assumption (JGA) produces the 1951 theory. Formulas for the pressure structure function and the pressure-gradient correlation are given, as are asymptotic formulas for the inertial and dissipation ranges. The values of constants and parameters in the new theory are evaluated using the JGA. The incompatibility of intermittency with the JGA causes the 1951 theory to have an opposite intennittency correction to inertial-range exponents as compared with the new theory.

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