Topology of trajectories of the 2D Navier-Stokes equations.

  title={Topology of trajectories of the 2D Navier-Stokes equations.},
  author={Jon Lee},
  volume={2 4},
In spectral form the 2D incompressible Navier-Stokes equations in a square periodic region will be represented by 430 complex Fourier amplitudes which correspond to isotropic truncation of the upper wave number 16. For small viscosity, we have found five equilibrium states I-V in the entire range of forcing; I-fixed point, II-circle, III-closed orbit, IV-torus, and V-chaos. The fixed-point equilibrium state is the laminar flow. As the forcing passes through a critical value, the fixed point… CONTINUE READING