Symmetries of plane Couette flow |
The Navier-Stokes equations for the plane Couette flow are equivariant under "shift-reflect" and "shift-rotate" transformations: |
By “equivariant” we mean that if u(x,t)
is a solution,
so are s1u(x,t),
s2u(x,t),
and s1s2u(x,t);
the four solutions are physically equivalent.
( to see examples of such symmetry-related solutions).
We refer to the space of velocity fields left invariant under the symmetry group
|