### Abstract

The triple velocity, the pressure-velocity, and the scalar-scalar-velocity correlations in incompressible turbulent shear flows and in passive scalar fields are studied by using the two-scale direct-interaction approximation, which satisfies the solenoidal condition of the velocity fields and systematically introduces the cutoff wave numbers. As a result, we obtain their expressions of the gradient diffusion type involving the effect of cross-diffusion. The model constants in the obtained expressions for the triple velocity and the pressure - velocity correlations are close to the values used in the turbulence models. The derived expression for the scalar-scalar-velocity correlation shows the complex dependence on the ratio R of the velocity length scale to the scalar one. As a special case of R= 1, we obtain its explicit expression whose model constant also agrees well with the numerically optimized value.

Original language | English |
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Pages (from-to) | 2636-2646 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 10 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes