Source Of Complexity

Lesson

Introduction
Matter of scale
- Scale of observation
- Structure of complex system
- Turbulent flow : visualization
- Wide range of scales in turbulent flow
Variability
Non-linearity
Introduction to differential equations
Governing equations
Different approaches
Exercises
To go further
Conclusion

Wide range of scales in turbulent flow

We have seen that the turbulent flow shows different structures (eddies) at different scales. The range of scale in turbulent flow depends on the Reynolds number :

$\textit{\textbf{Re}} = \frac{\text{Inirtial forces}}{\text{Viscous forces}} = \frac{UL}{\nu} \\ \quad \\ \text{The range of scale is given as:}\\ \frac{L}{\eta} = \textit{\textbf{Re}}^{3/4}$

U is the mean velocity of the object relative to the fluid.

ν is the kinematic viscosity.

η is the smallest scale

L is the largest scale

The Reynolds number flows of the natural environment is often very high, the small scale are of the order of millimeter

and the large of the order of kilometer → Re ≈ 1000000

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