Due to stretching of the small eddy's their spin increases because of conservation of impulse momentum (like a ballerina). This increases the kinetic energy of small structures at the expense of that in larger structures. This continues down to smaller scale until the scale of the structure is so small that energy is dissipated by viscosity (Kolmogorov length scale).

Due to stretching of the small eddy's their spin increases because of conservation of impulse momentum (like a ballerina). This increases the kinetic energy of small structures at the expense of that in larger structures. This continues down to smaller scale until the scale of the structure is so small that energy is dissipated by viscosity (Kolmogorov length scale).

Dear Avraham, good thankyou, the vortex stretching effect you describe must be part of the answer: conservation of angular momentum. But maybe there is another mechanism, something like a laminar instability? I am thinking of Kelvin Helmholz rollers that form in shear layers. I have met these on turbine blades that separate at low Reynolds. Niether the vortex stretching approach nor the kelvin helmholz idea can explain how the turbulence becomes 3D. This is because the vorticity is not turned by either Mechanism. They are essentially 2D tought processes. However, in a turbine blade passage normal vorticity from the boundary layers is partially turned as the primary flow is turned and creates streamwise vorticity. Maybe the vorticity becomes 3D when structures interact, maybe one eddy causes the turning of the vorticity in a fellow eddy. What do you think?

cheers Martin

Dear Martin, Indeed much of the "turbulence" of flows like shear layers is initially large scale hydrodynamic instabilities (waves) initiated by small perturbations, but amplified by vorticity dynamics. In general the most linearly unstable mode (fastest growing hydrodynamic instability) has a 2D structure. This can be proved (theorem see books such as Drazin on hydrodynamic instability). The perturbations that initialise the 2D instabilities can be: wall vibration, acoustic perturbation, wall roughness... However as the amplitude of the perturbations increases, one observes essentially 3D highly non-linear motions, which become what we commonly call "turbulence". In flat wall boundary layers, this starts with the formation of low speed streaks and the formation of hairpin vortices. These hair-pin vortices emerge from the boundary layer and breakdown into turbulent spots. Of course the type of dominant 3D non-linear motion that occurs depends on the type of flow considered (free jet, shear layer, boundary layer, swirling flow, pipe flow...). Here also details of geometry such as surface roughness is essential. Consequently there is a complex zoology of transition from 2D laminar instability to 3D chaotic motion. But when the Reynolds number is large enough there is always a cascade as described by the theory of Kolmogorov that transfers the energy down to small dissipative length scales. There vortex stretching is the dominant effect. 

Yours sincerely, mico

Dear Martin,  in my understanding the most fundamental mechanism is momentum self advection described by the  V/ . grad V/  term in the momentum equation.  Starting from this,  one can envisage many illustrative models (of different complexity levels) to explain how this works. Furthermore, forces on the rhs, mass continuity and energy conservation affect the process, leading to different cascades in different fluid scenarios (e.g., stratified, rotating, heated, etc.)

Piotr

Hello , 

AS Avraham Hirschberg said ,

You may benefit from those pictures .

Regards 

Salim salim Hamieh Could you please share the source?

This was discussed on RG earlier. The mechanism is self advection of momentum. To see this take expression like u,t + u u,x and assume

u ~ exp (i k x) . Then you can see right away that convective derivative generates tendency in twice larger wave number.

hope it helps. Piotr