# Expressions for pressure-velocity-gradient correlations

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## Abstract

The term for pressure-velocity-gradient correlation was initiated by Rotta's^{[21]} rewriting the correlation between the pressure fluctuation gradient and velocity fluctuation. However, it is very difficult to consider the effect of this term. Since Rotta's work, Launder et al.^{[7]} has made some estimates of this term. In this paper according to the equations for velocity fluctuation, the pressure fluctuation is solved so that the average value of the product of the pressure fluctuation and the velocity fluctuation gradient is obtained. Thus, the whole expressions for the pressure-velocity-gradient correlation are derived. The result explains that the limited expressions by Rotta and Launder are reasonable to a certain degree. The whole expressions in this paper are discussed respectively in two situations: one is without a separate consideration of large and small vortexes; the other is with a separate consideration of three kinds of vortexes. Therefore, the paper gives the whole expressions for pressure-velocity-gradient correlation to the Reynolds stress turbulence model^{[7]} and the three-vortex turbulence model^{[13]}.

## Key words

pressure-velocity-gradient correlation turbulence model theory second-order closure## Preview

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