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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?

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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.

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  • $\begingroup$ 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? $\endgroup$ – honeste_vivere Oct 1 '14 at 14:48
  • $\begingroup$ Superfluids are not your typical (classical) fluid, much like the liquid polymer case I cite; however they do exhibit turbulent flows. $\endgroup$ – Kyle Kanos Oct 1 '14 at 14:58
  • $\begingroup$ If you check the viscosity link in the body (to the Wiki page), you'll see an animation of two flows in which the only difference is viscosity; the lower viscosity fluid exhibits more turbulence than the higher viscosity flow. $\endgroup$ – Kyle Kanos Oct 1 '14 at 15:05
  • $\begingroup$ Ah, I see now why I was confused. I was aware of the quantized eddies/vortices, but I thought that implied a lack of turbulence since the eddies are all of the same size (and predictable), not random. I was also confused by the fact that if you managed to create a macroscopic eddy in a superfluid, I was under the impression that the eddy would remain the same size so long as the fluid remained a superfluid condensate. I thought that turbulence implied a transfer of energy from large-to-small scales through irreversible (viscous) interactions. $\endgroup$ – honeste_vivere Oct 1 '14 at 15:27

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