channelflow.org

I followed the first couple steps of John G's howto essentially verbatim and deviated only with respect to calculation of the poincare section.

I used the following script file, with eigenvalues already present, to generate my data:

#!/bin/bash
#This will hopefully generate all of the data I need to construct a poincare section of 
# the upper branch unstable manifold.

addfields 1 UB 1.12670e-05 e0 eq2_1
addfields 1 UB 1.26960e-05 e0 eq2_2
addfields 1 UB 1.43072e-05 e0 eq2_3
addfields 1 UB 1.61215e-05 e0 eq2_4
addfields 1 UB 1.81659e-05 e0 eq2_5
addfields 1 UB 2.04695e-05 e0 eq2_6
addfields 1 UB 2.30653e-05 e0 eq2_7
addfields 1 UB 2.59902e-05 e0 eq2_8
addfields 1 UB 2.92860e-05 e0 eq2_9
addfields 1 UB 3.29998e-05 e0 eq2_10
addfields 1 UB 3.71846e-05 e0 eq2_11
addfields 1 UB 4.19000e-05 e0 eq2_12
addfields 1 UB 4.72134e-05 e0 eq2_13
addfields 1 UB 5.52006e-05 e0 eq2_14
addfields 1 UB 5.99470e-05 e0 eq2_15
addfields 1 UB 6.75490e-05 e0 eq2_16

for i in eq2_*.ff ; do tag=${i#eq2_} ; couette -T0 0 -T1 400 -o data-${tag%.ff} $i ; done

I then created a parameter dependent flow field, that mixed two fields, or equivalently, john's e_theta.

I set theta to be pi/4, to get the strongest possible contribution from both fields. I then used poincare.cpp to calculate the intersections of each of the trajectories calculated in the script and saved them to disk. I then plotted them, and what resulted is what is in my blog.