Fabian Waleffe: Exact Coherent Structures in Plane Couette flows

Rigid-Rigid Plane Couette Flow steady state data:

This material is based upon work partially supported by the National Science Foundation under Grant No. 0204636. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

If you use this free data, please refer/cite the relevant publications in particular

Lower branch coherent states in shear flows: transition and control , by Jue wang, John Gibson and FW, to appear in Phys. Rev. Letters (2007)
Homotopy of exact coherent structures in plane shear flows by Fabian Waleffe, Physics of Fluids, 15, pp. 1517-1534 (June 2003).
Three-Dimensional Coherent States in Plane Shear Flows by Fabian Waleffe, Phys. Rev. Lett., Vol. 81, Number 19, pp. 4140-4143 (9 Nov 1998)
Exact coherent structures and their instabilities: Toward a dynamical-system theory of shear turbulence, pp. 115-128 in Proceedings of the International Symposium on ``Dynamics and Statistics of Coherent Structures in Turbulence: Roles of Elementary Vortices'', Shigeo Kida, Editor, National Center of Sciences, Tokyo, Japan, October 21-23, 2002
Transition threshold and the self-sustaining process, F. Waleffe and Jue ("Joy") Wang, in IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions, Tom Mullin and Rich Kerswell (Eds.), pp. 85-106, Springer, 2005. (Copyrighted by Springer...)

This data is for various UPPER and LOWER branch solutions at R= 400, 500, 1000, 2000, 4000 with fundamental wavenumbers in the streamwise x and spanwise z directions alpha=a and gamma=g (Lx=2 pi/alpha, Lz=2 pi/gamma).
The data is real in physical x (streamwise) and z (spanwise) space but given in Chebyshev space in the wall normal y direction with NC the total number of Chebyshev polynomials (0 to NC-1). The files are gzipped ASCII written in FORTRAN using

do ky=1,NC  
   do jz=1,nz 
      do jx=1,nx 
          write(13,110) u(jx,jz,ky)  
      enddo
   enddo
enddo
110  format((1x,G23.16))

with (NC, nz, nx) = ( 34, 32, 32) unless otherwise noted, so the data is in FORTRAN order (i.e. column-major).

R=400, (a,g)=(1.14, 2.5)

(data of figure 3 in the Tokyo conference proceeding paper listed and linked above.)

UPPER Branch UB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics
LOWER Branch LB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics

R=400, (a,g)=(0.5, 1)

LOWER Branch LB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics

R=400, (a,g)=(0.5, 2)

LOWER Branch LB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics

LOWER BRANCH data for (a,g)=(1,2) and R= 500, 1000, 2000, 4000. This data is in the same format as above but for different resolutions and the 3 fields (u,v,w) + the statistics file (y, U(y), u_rms, v_rms, w_rms) are lumped into a single .tar.gz file.

LB, R= 500, NC= 48, nz=32, nx=24 peek at the statistics
LB, R=1000, NC= 52, nz=48, nx=24 peek at the statistics
LB, R=2000, NC= 78, nz=48, nx=24 peek at the statistics
LB, R=4000, NC= 78, nz=48, nx=24 peek at the statistics

LOWER BRANCH data for (a,g)=(1.14,2.5) and R= 12000. This data is in the same format as above but for different resolutions and the 3 fields (u,v,w) + the statistics file (y, U(y), u_rms, v_rms, w_rms) are lumped into a single .tar.gz file.

LB, R= 12000, NC= 92, nz=64, nx=4 peek at the statistics

Watch the movies: The lower branch states have a single unstable eigenvalue and thus a one-dimensional unstable manifold. That unstable manifold leads to the laminar flow on one side and to turbulence on the other. The movies were made by Joy Wang using John Gibson's Channelflow code.

R=400, (a,g)=( 0.84, 1.67)

UPPER BRANCH UB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics

R=400, (,g)= ( 0.95, 1.67)

UPPER BRANCH UB, R= 400, NC= 34, nz=32, nx=32 peek at the statistics