11

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?

Qmechanic
  • 220,844
ergon
  • 753

1 Answers1

5

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.

Joce
  • 3,365