Fractal Flows and Tools for Tackling Turbulence |

A submission to the Summer of Math Exposition 4.

In this video, I introduce the topic of turbulence. I discuss what makes turbulence difficult to study, and I show how the scale invariance of turbulent flows (the fact that they look the same at different length scales) gives us a powerful tool to make progress in this field. I demonstrate the idea of scale invariance using examples, give a heuristic explanation for why it appears in turbulence, and then use it to quickly derive a famous result in the theory of turbulence.

0:00 Introduction
2:01 What is turbulence?
3:11 Why is turbulence hard?
7:56 Scale invariance
10:38 Navier-Stokes Equation
14:09 Kolmogorov's 5/3 Law
16:27 Calculation
19:15 The big picture
20:51 Credits

The smoke and laser demonstration was borrowed (with permission) from 3Blue1Brown and Physics Girl, whose videos with the demo are here:
3blue1brown:
   • Why 5/3 is a fundamental constant for turb...  
Physics Girl:
   • How to Make a SQUARE Vortex Ring! ft. 3blu...