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:
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (18391894)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (18031882)