Taylor-Green Vortex: Exact initial condition u=sin(x)cos(y), v=−cos(x)sin(y) on [0,2π]². This is the canonical test of turbulence codes — analytic at t=0, then nonlinear cascades develop. 2D NS: ∂ω/∂t + u·∇ω = ν∇²ω. In 2D, energy cascades upscale (inverse cascade) while enstrophy cascades to small scales (Kraichnan 1967). We use pseudo-spectral method with 2/3 dealiasing. Energy spectrum E(k) develops a −5/3 slope for enstrophy cascade range. Color = vorticity (red=CCW, blue=CW).