Exact solutions of NavierStokes 
uLM is the classic laminar equilibrium (steady state)  a linear profile (u,v,w) = (y,0,0):  
[click on figure to enlarge]
[L_{x}, L_{y}, L_{z}] = [5.51, 2, 2.51] cell, Re=400. All equilibria computed with Viswanath's NewtonhookstepGMRES search algorithm. Discretization is on a 32 x 35 x 32 dealiased grid. Truncated spectral coefficients are on the order 1e6. 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):  


Question: Why “lower branch,” “upper branch?”  