Taylor-Couette Flow

Anthony Youd

Hi,

I am trying to write a Fortran 90 program to solve the problem of axisymmetric Taylor-Couette flow between concentric cylinders, in the infinite cylinder approximation. I am using a 2nd order, finite-difference, vorticity-stream function formulation in cylindrical coordinates computing the azimuthal velocity on top of circular Couette flow. I use Crank-Nicolson time-stepping on the linear terms and Adams-Bashforth on the nonlinear terms with operator factorisation.

However, I am having a problem that is frustratingly difficult to track down. As a test I compute the velocity growth rates against known results, but an increase in the radial and/or axial truncation parameters does not cause the growth rate to converge to some value as you would expect. Changing the truncation always causes order 1 differences in growth rate. In fact, it appears that the growth rate is tending to zero as I increase the truncation. However, the code always predicts the correct critical Reynolds number for the onset of Taylor vortices, no matter how good or bad the truncation, and the general shapes of all the variables are correct.

You would expect that a decrease in the truncation would cause a worsening growth rate.

The code is nonlinear but I have linearised it to help debugging, as well as trying other parameters (radius ratio, Reynolds number etc.). From the tests I have done it seems that the basic underlying diffusion equations (without nonlinear terms) as well as the Poisson equation on their own are correct. I am pretty sure there are no typos having checked the code plenty of times and the time-step is not too large.

Does anybody have any ideas as to what the problem could be here? Has anyone come across anything like this in any other problems? Any suggestions at all are welcome.

I hope I haven't been to vague in describing the above but I can post further details or parts of the code if that would help,

Thanks in advance,

Anthony.