One definition of turbulence:**

"Strongly disordered motion of a fluid accompanied by chaotic wide-spectrum fluctuations of all flow characteristics".

Landau-Hopf Model (1940s):

•There is an "energy cascade": large-scale partially ordered structures (unstable)—>>generate smaller, less-ordered structures—>>smaller still, etc.

•Energy is transferred from large to small.

•Cascade Model was used by Kolmogorov who formulated quantitative results based on it.

This model is now considered to have little foundation (wrong?) because large-scale organized structures play a very important role in turbulent flows: they are

generated by an "inverse energy cascade"—>>small to large, just the opposite of Landau's picture.

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**This page taken from [3].