# Is turbulence due to the inertia of the fluid?

Turbulence is the time-dependent chaotic behavior seen in many fluid flows.

Why is it generally believed that turbulence is due to the inertia of the fluid?

The key is the Reynolds number, $$Re=\frac{\rho LV}{\mu}=\frac{LV}{\nu}\tag{1}$$ where $L$ and $V$ are characteristic lengths and velocities of the particular problem and $\mu$ & $\nu$ are the dynamic & kinematic viscosities, respectively.
If you multiply (1) by $\rho LV/\rho LV$, you get $$Re=\frac{\rho L^2V^2}{\mu LV}$$ The numerator is the inertial force while the denominator is the viscous force. When $Re$ is small, the fluid flow is described as Laminar. When $Re$ is large, the fluid flow is described as turbulent. Since $Re$ is large for large inertial force (relative to the viscous force), we can say that inertia causes turbulence.
However, elastic turbulence in liquid polymers can occur when $Re$ is small, suggesting that the cause$\leftrightarrow$effect from above may not actually be correct, at least for the case of polymers.
• Perhaps I am mistaken here, but I am confused as to why it is thought inertia matters. I ask because according to your equation, R$_{e}$ $\rightarrow$ $\infty$ for $\mu$ $\rightarrow$ 0, right? However, without viscosity can a fluid be turbulent? I thought superfluids always exhibited laminar flows? Did I miss something? – honeste_vivere Oct 1 '14 at 14:48