Kolmogorow Scales
 

hi,

I ve a few question about the Kolmogorow scales which are briefly described here

http://en.wikipedia.org/wiki/Kolmogorov_microscales

1. length scale:
- Is the length scale the size of the smallest turbulence encountered?
and
- Have the mesh cells to be all of the same size or even smaller in DNS (direct numerical simulation)?

2. time scale:
- What is the meaning of the time scale?
- What is it good for? Does it have an influence on the simulation time steps?

3.velocity-scala:
- What is it good for?

greetings
maybee

1.
- In turbulent flows a spectrum of turbulent structures exists, from very large to very small ones. turbulent energy is transported from large scales to small ones in a sequence called "cascade of energy". the smallest possible turbulent structure in a continuum flow has a length scale called kolmogorov. These scales just dissipate the energy they get. in other words there is no smaller scale to receive their energy.
- yes, the size of elements should be as small as kolmogorov length scale in case of DNS simulations.

2 & 3.
- for each turbulent structure and at any length scale a time scale can be defined which refers to "one turnover" of that structure. in other words one period in which the turbulent structure changes and then return to its initial state.
- velocity scale is defined as ratio of length scale to time scale.
- one application of these scales is to approximate and simplify the governing equations so as to find order of magnitudes of variables. this is particularly useful in development of new models explaining a specific phenomenon in fluid flow e.g. a new combustion model, a new two-phase model, etc.

regards

The Kolmogorov length scale is the smallest wavenumber scale where turbulent kinetic energy is dissipated by viscosity.

Energy cascades from the large scales to the small scales at a rate of k^-5/3
where k is wavenumber.

Once the scales are small enough, velocity gradients (strain rates) become large and molecular viscosity can act to dissipate the turbulent kinetic energy.

just few words...

- the energy cascade has an inertial slope at high Re and far from walls... otherwise the -5/3 law is not observable.
- The Kolmogorov lenght scale is the smallest dissipative turbulence scale but dissipation starts well before, at the Taylor lenght micro-scale