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.
Read more about this topic: Reynolds Stress
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)