I got the sentence from w. Rodi's book TURBULENCE MODELS AND THEIR APPLICATION IN HYDRAULICS that " eddy viscosity proportional to a velocity characterizing the fluctuation motion and to a typical lenth of this motion which prandlt called mixing length" i want to know what is the meaning of velocity characterizing and typical length and mixing length.

unit of viscosity are m2/s. this therefore translates to being proportional to a length, m * a velocity, m/s with added constants.

therefore to quantify the additional stresses caused by the tubulent motion (reynold stresses) we must choose an appropriate viscosty and as seen above this will be found from choosing an apprapriate length and velocity scale for the turbulent motion.

the velocity scale is often chosen as the sqrt(of turbulnt energy) so a tranport equation can be solved for KEt.

the length sclae is more difficult to choose as high reynolds nuber turbulence has a range of scales present. we therefore usually choose the integral scale which is the size of the largest eddies. (the justification of choosing the largest sclaes is based on the idea of an energy cascade where the small scale motions is determined by the energy passed to them from the largest scales).

the term mixing length originates from prandtls orginal model, where a velocity gradient dudy, over a small distance l, is said to cause fluctuations of order l*dudy. the fluctuatons cause momentum transfer and serve to mix the flow.

hope this helps.

What you mean by dudy and energy cascade

you should look in a turbulence book at the ideas of kolmogorov and the -5/3 law - this will explain the energy cascade. it is basically the idea that large turbulent scales will pass energy to smaller scales and so on, unitl viscosity dissipates the smallest scales. (one of the best books is by tennekes and lumley).

by dudy i meant the velocity gradient, i.e. change in velocity / change in distance.

i will contect you after studyind books within 10 days may i have ur email address thanks for help