# Turbulence in fundamental particles

We know that when fluids move fast enough they create turbulence. So, my question is: Is it true for mass-less or negligible mass particles also, do they also show turbulence when accelerated to extremely high speeds?

• In what medium? – knzhou Apr 7 '18 at 11:47
• knzhou I am particularly interested in vacuum because it is less hard than other cases – Bhaskar Pandey Apr 8 '18 at 15:46

Estakhr's decomposition is a mathematical technique to separate the average and fluctuating parts of Relativistic Turbulent Flows.

$${\overline{U}^{\mu}=\lim_{\tau\rightarrow\infty}({\frac{1}{\tau}}\int_{\tau_{o}}^{\tau}U^{\mu} d\tau)}$$

Where the $\tau$ is proper time.

$${U^{\mu}=\overline{U}^{\mu}+U'^{\mu}}$$

Where the $\overline{U}^{\mu}$ denotes the proper time average called steady component and $U'^{\mu}$ is fluctuating part.

There are No turbulence، When fluctuating part is equal to zero.

$$U'^{\mu}=0$$

• I really liked your answer, but it would be amazing if you could explain the integral and how it is derived (maybe not derivation but intuitive sense of it) – Bhaskar Pandey Apr 8 '18 at 16:03