# Meaning/picture of the statement: "Turbulent flow is chaotic. However, not all chaotic flows are turbulent"

Wikipedia states that

Turbulent flow is chaotic. However, not all chaotic flows are turbulent.

Someone give a picture for that?

• You want a picture that shows that not all chaotic flows are turbulent? Apr 3 '14 at 11:21
• A picture or explanation whatever you like.
– user28737
Apr 3 '14 at 11:47

It's largely a matter of definition. Here are some quotes.

From Springer Reference:

Definition There is no universally recognized definition of chaotic flows. Flows with properties that are neither constant in time nor presenting any regular periodicity are normally referred as chaotic. Fluid turbulence is generally found to be chaotic. It is also random, dissipative, and multiple scaled in time and space. It is a complex system of infinite degrees of freedom.

A paper full of state diagrams (but rather heavy on the math) for transitions to chaotic flow: https://tspace.library.utoronto.ca/bitstream/1807/25484/1/Transition%20to%20chaos%20in%20converging-diverging%20channel%20flows.pdf

And finally, a nice discussion at quora.com (registration apparently required)

As Piyush Grover pointed out, a chaotic flow has to have mixing by definition. The following answer assumes 'chaotic' to mean 'random' which is technically incorrect. But I've decided to leave it here anyway, because I think that's what the OP meant. However, I still think that you won't observe a k^(-5/3) spectrum in the case of chaotic advection.