4. Exact solutions of Navier-Stokes

4a. Exact solutions: “Old” equilibria

The next two frames show the known equilibria (steady states) of plane Couette flow.

uLM is the classic laminar equilibrium - 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 (computed following Waleffe):
[lower-branch equilibrium]       
    [upper-branch equilibrium]
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