davidgalbraith

Turbulence (James Reuther email)

James Reuther on Turbulence:

“There is an energy cascade from larger eddies to smaller eddies until the Kolmogorov scale is reached and the viscous dissipation can play an active and direct role in converting the energy from kinetic form to thermal form with maximum entropy production. It is also shown that there is a level of self similarity in the intermediate flow features or vortical structures between the largest length scale and the Kolmogorov scale in what is called uniform turbulence (these rules do not apply when a physical boundary is present influencing the structures). However the self similarity is not complete, and only works on the lowest order statistical moments. All higher order moments due not show a constant correlation and hence show that there differences in the details of the flow features that are in fact scale dependent. ”

“The analogy that I like to use is gears. Imagine a set of gears, one very large gear surrounded by sets of ever smaller gears. As the largest gear turns it turns its immediately neighboring gears in the opposite direction who then turn their neighboring smaller gears and so on until the smallest gear simply turns the air or fluid it sit in heating it up by friction. In my thought analogy, the kinetic energy in the largest gear is transferred to ever larger number of smaller gears until the enormous number of the smallest gears individually have such little kinetic energy that it is easy to convert it into heat directly and thereby provide enough total friction that power can be input into the largest gear without any acceleration of the whole system. The laws of fluid dynamics controls the size and number of neighboring gears at each scale, and a look across all given scales shows that the gross relationship of the number of surround gears and their relative size is the same irrespective of the scale viewed. However, the details, such as the shape and number of gear teeth, as well as their size relative to the gear size is dependent upon the individual scale that is viewed. These details are the higher order moments. Hope this helps. If you want much more comprehensive literature I can send you more references.”