# Why do large eddies in turbulence break-up

This is probably a silly question. But, Why do large turbulent eddies break up into smaller ones?

## A possible argument

Why can't they (large eddies) retain their size and gradually diffuse instead of breaking up. Does something make these large eddies unstable (similar to instability of laminar streamlines which causes transition to turbulence), forcing them to break up?

What is it that determines the "break up instant" of an eddy?

In separated flows, a vortex is shed when "enough" vorticity is accumulated. Does this argument hold true for turbulent eddies too? i.e.; Do turbulent eddies break up due to accumulation of vorticity?

• Think about the meaning of viscosity. It's momentum flux transport across a boundary orthogonal to the local linear momentum, e.g., x-momentum transport across the yz-plane. Without viscosity, can you break up a large vortex? – honeste_vivere Jan 12 '19 at 21:33
• @honeste_vivere , I couldn't grasp what you meant. I think an eddy breaks due to "some" instability. Diffusion due to viscosity is always occurring. If diffusion was to be the only mechanism, then the eddies would die down only after a long time. – Zxcvasdf Jan 15 '19 at 6:02
• If you remove diffusion and viscosity, will the eddies break up? – honeste_vivere Jan 15 '19 at 16:34
• I really have no basis for answering this. Probably yes, they might still break. What do you think would happen? By the way, I don't think there would be turbulence in the first place without viscosity. – Zxcvasdf Jan 16 '19 at 4:38
• Actually, it turns out that eddies don't always break up. In two dimensional turbulence eddies get bigger and bigger. The canonical example of this is Jupiter's red spot, which is an eddy that is bigger than the diameter of the earth and has been stable for centuries. – Steven Mathey Feb 21 '19 at 15:54