Taylor Couette Instability
 

I have been trying to get my canned finite volume code simulate the Taylor Couette Instability. This occurs when the flow between 2 rotating cylinders goes unstable after a certain value of the Taylor number is reached. Basically if the outer cylinder is rotating slower than the inner one by a certain ratio, the flow should go unstable. This is often cited as the best validation of a code.

Does anyone have experience doing this? At what Taylor numbers could they achieve the instability? How long did it persist? What were the sizes of the cells?

Re: Taylor Couette Instability
 

Have a look in the book by Drazin & Reid on Hydrodynamic stability it contains the marginal stability curves and everything else you need to know.

The instability persists as long as you keep the cylinders rotating - when you are above the neutral curve there exists more than one steady state (in the simplest instance) solution. One of these solutions is Couette flow which is the base state which goes unstable and the other is the Taylor flow which is a periodic set of vortices which bifurcates from the base state at the critical Taylor number,

Tom.

Re: Taylor Couette Instability
 

Hi, Can I ask you if you are using cylindrical coordinate code? And how do you work with the boudary?( The Taylor instability has a linear solution for an infinity long cylinder).

Thanks

Re: Taylor Couette Instability
 

Another excellent source for information: Chossat & Iooss: The Couette-Taylor problem.

-- Jarmo

Re: Taylor Couette Instability
 

Thanks all for yr comments. I have been reading Drazin and Reid for the problem, and am well aware of what should happen theoretically. Unfortunately, this does not happen in the simulation. I do not see any major 3D structures in the flow.

I am imposing periodic boundary conditions in the axial direction. The size of my domain is 10* the separation between the cylinders.

Re: Taylor Couette Instability
 

As the first instability of circular Couette flow, toroidal Taylor vortex cell will appear side by side in the axial direction, which is roughly square in shape crossing the gap. Simulation of Taylor vortex needs proper form of artificial perturbation imposed for some time in most cases, and with proper grid numbers. Also, be sure your Taylor number ( or equivalent Reynolds number ) be greater than (not nearby) the critical one.

Re: Taylor Couette Instability
 

Actually being able to pick up the neutral stability curve is a good test of a computer code (providing the bifurcations are supercritical of course). You can also test the code against weakly nonlinear theory which it should agree with.