Reynolds Stress - Definition

Definition

For a homogeneous fluid and an incompressible flow, the flow velocities are split into a mean part and a fluctuating part using Reynolds decomposition:

with being the flow velocity vector having components in the coordinate direction (with denoting the components of the coordinate vector ). The mean velocities are determined by either time averaging, spatial averaging or ensemble averaging, depending on the flow under study. Further denotes the fluctuating (turbulence) part of the velocity.

The components τ'_ij of the Reynolds stress tensor are defined as:

with ρ the fluid density, taken to be non-fluctuating for this homogeneous fluid.

Another – often used – definition, for constant density, of the Reynolds stress components is:

which has the dimensions of velocity squared, instead of stress.