Exact solutions of Navier-Stokes |
| uLM is the classic laminar equilibrium (steady state) - a linear profile (u,v,w) = (y,0,0): | ||
![[laminar equilibrium]](Images/uLMbig.png) |
[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]](Images/uLBbig.png) |
![[upper-branch equilibrium]](Images/uUBbig.png) |
|
| Question: Why “lower branch,” “upper branch?” | ||
 |
||