Hi Gents,

I am a research student and working on a fluid mechanic project. I am puzzled by a basical question, which is "what causes turbulence?"

Could you give me some hints or recommend some references?

Many thanks,

nonlinear dynamics

when momentum is much greater than viscous effects

Hi,

we can generally say that turbulence is caused by undamped perturbations which lead to caos (nonlinear dynamic). That is, instability in a nonlinear system, the fluid.

The single most important parameter that will give you informations about the behaviour of the perturbations (if they will be damped or not) is, as probably you already know, the Re number. It is a measure of the relative importance of convective and viscous terms in N.S. eqnuations (their ratio).

If the Re number is low enough (for a particular flow) every perturbation will be damped and there will be no turbulence (that is the viscous term is strong enough to damp them). If this is not the case, the perturbations will not be damped and will retain "some energy" which in turn will govern the evolution of the flow; in this case the viscous term will still be working but not so strongly to dissipate all the energy.

I'm not so expert in this but, in my knowledge, there is no way to have turbulence without entropy production, the cause of the perturbations; but if some perturbation alreqady exists, it will be sustained even without viscous terms (of course the behaviour will be different, due to a different governing equation).

I hope this helps

> there is no way to have turbulence without entropy production

There is no way to have non-constant viscous flow without entropy production.

Thank you so much for your opinions. Please add anything if you think that is helpful.

Thanks a lot,

Francis

I think it's necessary to add that you need a kind of flow which can exhibit instability (growing of perturbations). Usually for this you need a cross-stream velocity gradient, i.e. shear flow. Please correct me if I'm wrong, but AFAIK turbulence is always associated with shear.

As stated before i'm not so expert in this, so could you explain more exactly what you mean with:

"There is no way to have non-constant viscous flow without entropy production"

What i said is that to have a perturbation you need entropy production or a flow with some perturbation in its initial condition. But how this initial perturbation is introduced if not via entropy production?

For entropy production i mean every single positive coefficient in the entropy equation which in turn can produce non-normal stress (only normal stress are well known to not produce turbulence) in the flow so potentially non-stable perturbations. Is it wrong?

Heat production is stress * strain. This is an irreversible process, hence it produces entropy. Turbulence occurs when stress is very small compared to strain (high Reynolds number). The Euler equations have no turbulence or viscous stress and they predict no entropy production. If we could take laminar Navier-Stokes flow all the way to the Euler limit, the entropy production would go smoothly to zero. With turbulence, things are much more interesting.

"The Euler equations have no turbulence or viscous stress and they predict no entropy production"

This is not actually true. Euler equations are not irrotational, in fact there could be vorticity (for example produced by a cuvilinear shock wave) and so there should be the nonlinear dynamic.

Check the Entropy equation

http://www.cfd-online.com/Forum/main.cgi?read=61471

Laminar Navier Stokes is just Navier Stokes and, as stated before, in the limit of zero viscosity you will not recover the zero entropy production.

I still don't understand the non-costant viscosity issue. What you mean for it?

Anyway i agree with you in this: with turbulence is much more interesting

I was referring to *incompressible* Euler equations, sorry. Take mu=0 and div(u)=0 in your entropy equation. You are left with nothing but heat diffusion and the internal term (which have nothing to do with fluids). So the incompressible Euler equations have no entropy production.

As for varying the viscosity, suppose you have laminar NS flow and you want to take the Euler limit. If you can't adjust the viscosity, then you would have to go to infinite velocity and of course entropy production will go to infinity as you do this. If you reduce the viscosity, viscous dissipation (equivalent to entropy production) will drop smoothly until you transition to turbulent flow. If it didn't become turbulent (follow the unstable equilibrium of laminar flow), then entropy production would go smoothly to zero.

Ok, now i completely agree