[FluidKo]

Hello everybody~!

I'm watching turbulence lecture by professor Chin. Jen. Chang.
In his lecture, I have a question.
Below is link for where I can't understand from his lecture.
https://youtu.be/u23Nt3857zU?list=PL...PX2o4TX&t=4215
In this video, he has said
1. "Small eddy will grow back to the LARGER eddy and becomes SLOWER in motion"

2. "Turbulence is not always cascade. Turbulence can occur from small and go to LARGER eddy."

I can't understand why turbulence can go upstream of energy cascade.
And also what I know is that as bigger eddy, velocity of eddy(fluctuation) becomes faster.
But in 1. sentence, he has said larger eddy is slower. This is not corresponed with what I know.

Can you let me know why turbulence can go upstream of energy cascade and larger eddy can become slower?

Thank you~!

[aerosayan]

I was seeing Steve Brunton's lecture on RANS and he mentioned a similar thing. I don't know the mathematical answer, but intuitively we can kind of understand that an unstable eddy can cause more eddies to be generated. Where a sufficient number of small eddies are formed, they will impact the mean flow of the fluid, and actually cause it to become more turbulent.

Few example might be the case of dimples on a golf ball, or ice formation on wings, or even a small portrusion in the heat shield of NASA's space shuttle which required the astronauts to fix it in space.

In the last case, NASA engineers were worried that the small portrusion/gap in the heat shield tiles will lead to turbulent flow and thus cause superheated boundary layer flow near the body of the space shuttle, and blow it up.

[FluidKo]

Originally Posted by aerosayan

I was seeing Steve Brunton's lecture on RANS and he mentioned a similar thing. I don't know the mathematical answer, but intuitively we can kind of understand that an unstable eddy can cause more eddies to be generated. Where a sufficient number of small eddies are formed, they will impact the mean flow of the fluid, and actually cause it to become more turbulent.

Few example might be the case of dimples on a golf ball, or ice formation on wings, or even a small portrusion in the heat shield of NASA's space shuttle which required the astronauts to fix it in space.

In the last case, NASA engineers were worried that the small portrusion/gap in the heat shield tiles will lead to turbulent flow and thus cause superheated boundary layer flow near the body of the space shuttle, and blow it up.

Now you mention it, I think small eddies can induce large eddies.
I think if many small eddies that is hooked to large eddy affect mean flow together, they can make mean flow to be turbulence.
If mean flow is becomes turbulent flow, it will have largest length scale because largest eddy is induced from mean flow.

In conclusion
1. Small eddy can induce large eddies by affecting mean flow. We call it going upstream of energy cascade.
2. If mean flow becomes turbulent flow, then it will have largest length scale and produce smaller eddy by hooking its own eddy ring. This is normal energy cascade.

Thank you~!

[FMDenaro]

You are talking about the energy backscatter, a specific feature you can see in some turbulent flows.
Just as example, Hurricanes are a case where a big large eddy is created from sources of energy at smaller lenght. That happens especially in quasi-2d flow where the action of the stretching is disregardable.

[FluidKo]

Originally Posted by FMDenaro

You are talking about the energy backscatter, a specific feature you can see in some turbulent flows.
Just as example, Hurricanes are a case where a big large eddy is created from sources of energy at smaller lenght. That happens especially in quasi-2d flow where the action of the stretching is disregardable.

Why stretching is disregardable for quasi-2d flow?
Because vortex stretching is carried out with 3 dimensional?

[FMDenaro]

Originally Posted by FluidKo

Why stretching is disregardable for quasi-2d flow?
Because vortex stretching is carried out with 3 dimensional?

Yes, the stretching of vorticity vanishes in the 2d limit.

[sbaffini]

The fact that a larger eddy then becomes slower is just angular momentum conservation. Think about the classical skater example.

I suggest everyone in CFD to try the experiment of performing a laminar, bi-periodic, unsteady computation initializing the flow field with a fully random velocity field. From its visualiztion it is super clear how energy flows from small to large scales and how it happens.

BUUUT, in real 3D turbulent flows, it is quite far from obvious what is the route and what are the mechanisms. I mean, we don't even know exactly how the forward cascade happens in a number of flows. Also, the backward cascade is in place together with the forward one, they happen at the same time, probably even at the same place (within the overlap of the length and time scales involved).

A typical example of backward cascade in 3D is near the wall in turbulent boundary layers, where most energy is contained in wall streaks, which then relax into larger structures as they move away from the wall. But this is completely because of the near wall. A completely different mechanism is in place for, say, homogeneous turbulence.

[FluidKo]

Originally Posted by sbaffini

The fact that a larger eddy then becomes slower is just angular momentum conservation. Think about the classical skater example.

I suggest everyone in CFD to try the experiment of performing a laminar, bi-periodic, unsteady computation initializing the flow field with a fully random velocity field. From its visualiztion it is super clear how energy flows from small to large scales and how it happens.

BUUUT, in real 3D turbulent flows, it is quite far from obvious what is the route and what are the mechanisms. I mean, we don't even know exactly how the forward cascade happens in a number of flows. Also, the backward cascade is in place together with the forward one, they happen at the same time, probably even at the same place (within the overlap of the length and time scales involved).

A typical example of backward cascade in 3D is near the wall in turbulent boundary layers, where most energy is contained in wall streaks, which then relax into larger structures as they move away from the wall. But this is completely because of the near wall. A completely different mechanism is in place for, say, homogeneous turbulence.

Then slower means slow angular momentum not slower velocity right?

[sbaffini]

No, it actually means the same angular momentum. Thus, if the fluid gets away from the rotation center it needs to slow down. In very simple terms, if r times V needs to be constant and r increases then V needs to reduce. In 3D fluid flows the matter is considerably more complex than that, but that's the main point.

EDIT: Yet, to be honest, I haven't watched the video, as now I can't, so I can't say exactly what is mentioned in it.