| mean specific body force; |
| symmetric part of; |

| mean specific internal energy; |
| mean production associated with; |

| production associated with; |
| mean flux associated with; |

| specific turbulent kinetic energy; | , | fluxes associated with and, respectively; |

| mean heat flux; |
| turbulent heat flux; |

| mean specific energy supply; |
| Reynoldsâ€™ stress; |

| mean specific entropy supply; |
| transpose; |

| mean Cauchy stress; |
| mean velocity; |

| mean internal friction; |
| arbitrary quantity; |

| material derivative of w.r.t. | , | mean and fluctuating values of, respectively; |

| mean density of the solid grains; |
| specific turbulent dissipation; |

| mean specific entropy; |
| mean volume fraction; |

| mean entropy production; |
| mean entropy flux; |

| turbulent entropy flux; |
| any mean orthogonal rotation of a granular RVE; |