- 2019 American Physical Society.. The objective of this work is to develop the framework and governing equations needed to analyze the interactions and spectral distribution of internal energy in a manner similar to that of a kinetic energy analysis. To emulate the role of velocity in a kinetic energy analysis, a variable (p, where p is pressure) is introduced to enable the examination of internal energy dynamics. Evolution equations for the mean and fluctuating components of are derived. These equations enable the precise examination of mean-turbulent flow internal energy interactions, internal-kinetic energy exchange, and the spectral distribution of internal energy.