The Navier–Stokes solver (ns2d.py)

Pseudo-spectral 2D Navier–Stokes in vorticity form on L=2π: vorticity ω advanced in Fourier space, streamfunction from ∇²ψ=-ω, 2/3 dealiasing, integrating-factor RK4 on the viscous term. Band-limited random initial vorticity at fixed seed, normalized to a target initial enstrophy.

)} Pseudo-spectral 2D Navier–Stokes in vorticity form on L=2π: vorticity ω advanced in Fourier space, streamfunction from ∇²ψ=-ω, 2/3 dealiasing, integrating-factor RK4 on the viscous term. Band-limited random initial vorticity at fixed seed, normalized to a target initial enstrophy.

)} Pseudo-spectral 2D Navier–Stokes in vorticity form on $L=2\pi$ : vorticity $\omega$ advanced in Fourier space, streamfunction from $\nabla^2\psi=-\omega$ , 2/3 dealiasing, integrating-factor RK4 on the viscous term. Band-limited random initial vorticity at fixed seed, normalized to a target initial enstrophy. The solver underlies Pillar I's invariants and budget, the reference viscous branch of Pillar IV, and the pinned reference table (Appendix Appendix X). Full source is shipped as ns2d.py.