Exact solutions of Navier-Stokes

uLM is the classic laminar equilibrium (steady state) - a linear profile (u,v,w) = (y,0,0):
[laminar equilibrium] [click on figure to enlarge]

[Lx, Ly, Lz] = [5.51, 2, 2.51] cell, Re=400.

All equilibria computed with Viswanath's Newton-hookstep-GMRES search algorithm. Discretization is on a 32 x 35 x 32 dealiased grid. Truncated spectral coefficients are on the order 1e-6. Each field is a fixed point of the CFD algorithm to about the same accuracy.

uLB, uUB are the Nagata lower and upper branch equilibria (derived independently by Waleffe):
[lower-branch equilibrium]       
    [upper-branch equilibrium]
Question: Why “lower branch,” “upper branch?”
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