Averaging and The Reynolds Stress
To illustrate, Cartesian vector index notation is used. For simplicity, consider an incompressible fluid:
Given the fluid velocity as a function of position and time, write the average fluid velocity as, and the velocity fluctuation is . Then .
The conventional ensemble rules of averaging are that
One splits the Euler equations or the Navier-Stokes equations into an average and a fluctuating part. One finds that upon averaging the fluid equations, a stress on the right hand side appears of the form . This is the Reynolds stress, conventionally written :
The divergence of this stress is the force density on the fluid due to the turbulent fluctuations.
Read more about this topic: Reynolds Stress
Famous quotes containing the words reynolds and/or stress:
“If you have great talents, industry will improve them: if you have but moderate abilities, industry will supply their deficiency.”
—Sir Joshua Reynolds (1723–1792)
“In the stress of modern life, how little room is left for that most comfortable vanity that whispers in our ears that failures are not faults! Now we are taught from infancy that we must rise or fall upon our own merits; that vigilance wins success, and incapacity means ruin.”
—Agnes Repplier (1858–1950)