Kolmogorov’s Theory

Yesterday, I heard about Kolmogorov for the first time. None of the Transport Phenomenon text books of my time mentioned his name, which is not so surprising; because he was a Russian.  In 1941, Andrei Kolmogorov published a paper, which founded the mathematical analysis of turbulence.  While turbulence can be felt and even seen, it is extremely difficult to grasp mathematically.

Turbulence results in eddies of many different sizes.  The eddies are unstable and breakdown rapidly. The larger sized eddies transfer their energy to smaller sized eddies and so on till they finally breakdown and all energy is dissipated. Kolmogorov developed a formula for this energy transfer. This is an extremely simplified explanation and the mathematics can get scary even for engineers.

E(k,ψ) = Ck^-5/3ψ^2/3

Kolmogorov’s Theory is useful for simulating, predicting and understanding mixing patterns in agitated vessels. Always good to keep learning new things.