In high Reynolds numbers we have turbulent flow. This is because the inertial forces are much greater than the viscous forces. I understand inertial forces to be actually the fictional forces due to the momentum of the moving fluid. And viscous to be the forces that drag each layers together. But why when inertial forces are too high than the viscous forces, there is turbulence? Why don't the molecules just continue to move laminarly due to their momentum? I can assume the viscous forces are not very strong in high speeds (in high inertial forces) to keep them together to form a laminar flow? But again, why they result in irrational movement after the effect of viscous forces is not anymore considerable? As a mechanical analogue, if I have balls attached together and make them travel linearly, and remove their between them attachment, they can continue to travel linearly. But what happens in fluid molecules that turbulence is created?

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    $\begingroup$ This has to be with stability. If you have a time independent solution of the Navier-Stokes equations, you can consider a small perturbation and study how this perturbation evolves in time. What you find is that at low Reynolds numbers the perturbation will decay, and there is a critical Reynolds number above which you'll excite a mode that will not die down. If you then increase the Reynolds number more another mode will appear that does not die down and the more you increase it the faster new modes appear. $\endgroup$ May 12, 2016 at 1:20
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    $\begingroup$ @CountIblis: your comment should be an answer $\endgroup$
    – nluigi
    May 12, 2016 at 9:21
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    $\begingroup$ I have one more thing to add to what @CountIblis said. The Navier-Stokes equations are non-linear, so they can have more than one solution for a given situation. If a steady time-independent flow is one solution, there can also be a turbulent (non-steady) flow. Whichever is more stable determines the flow that will prevail. $\endgroup$ May 12, 2016 at 10:45
  • $\begingroup$ Related: physics.stackexchange.com/q/15738/2451 , physics.stackexchange.com/q/56496/2451 and links therein. $\endgroup$
    – Qmechanic
    May 13, 2016 at 9:03

1 Answer 1


The role of viscous forces with respect to turbulence is analogue to the one of diffusion for mixtures: it sets a scale below which it smoothes out gradients. So there are no vortices smaller than this. When this scale is much smaller than the scale of the experiment, tubulence can happen.

Turbulence is not linked with a peculiarity of the molecules. It can happen in any fluid, gas or liquid, when an inhomogeneity triggers an instability—and we find that situations as simple as two layers of fluid moving in parallel motion on top of one another are unstable, see Kelvin-Helmholtz instability.

But turbulence it has its very peculiar features in a 3D continuum: geometry is essential to it. It starts with 2D like structures, so elongated vortices. When they are close together, they interact and roll around one another. Because in 3D nothing forces them to be perfectly aligned, they will "cut" one another at intervals, generating smaller, even less aligned vortices. In turn, these will interact and a whole cascade of smaller and smaller vortices is generated, until you reach the viscous scale.


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