Modeling the pressure gradient–velocity correlation of turbulence

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Abstract
The modeling of the pressure gradient–velocity correlation of turbulence is considered. Two distinctly different approaches have been proposed in the turbulence literature: one in which the pressure gradient–velocity correlation is decomposed into a pressure‐strain correlation and a pressure‐diffusion correlation, and another in which the pressure gradient–velocity correlation is split into its deviatoric and isotropic parts. By examining the limit of two‐dimensional turbulence, it is demonstrated that the models obtained from the former approach are inconsistent with the Navier–Stokes equations in a fundamental way, whereas the models obtained from the latter approach are not. Consequently, it appears that the direct modeling of the pressure gradient–velocity correlation in its deviatoric and isotropic parts should be favored. The implications that this result has on turbulence modeling are discussed briefly.

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