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====== How to find invariant solutions ====== The channelflow ''findsoln'' utility will compute unstable equilibria, traveling waves, and (relative) periodic orbits of plane Couette or channel flows. Here are a few examples of usage. ===== periodic orbit of plane Couette flow ===== 1. Generate a random velocity field with ''randomfield'' <code> gibson@theaetetus$ randomfield -m 0.50 -lx 0.875 -lz 0.6 -Nx 32 -Ny 33 -Nz 32 u0 </code> This will construct a random velocity field in file ''u0.h5'', in a Lx x [-1, 1] x Lz periodic box with Lx = 2 lx pi = 1.75pi and Lz = 2 lz pi = 1.2 pi (the plane Couette minimal flow unit of Hamilton, Kim, Waleffe JFM 1995) with a 32 x 33 x 32 collocation grid (which is a lower resolution than I like for these calculations, but will result in a fast-running demo.) The velocity field u0 will be incompressible and have u=0 BCs at the wall, and will have an L2Norm of 0.50. <code> gibson@theaetetus$ fieldprops -n u0 Ubase mean == 0 --------------Norms--------------------- L2Norm(u) == 0.5 L2Norm(u[0]) == 0.421913 L2Norm(u[1]) == 0.252757 L2Norm(u[2]) == 0.0900201 LinfNorm(u[0]) == 1.22587 LinfNorm(u[1]) == 0.719326 LinfNorm(u[2]) == 0.32997 L2Norm3d(u) == 0.489487 divNorm(u) == 2.42575e-15 bcNorm(u) == 2.99093e-16 </code>
