The Taylor-Green vortex (G.I. Taylor & A.E. Green, 1937) is one of the most
famous exact initial conditions in fluid dynamics: a simple, smooth array of
counter-rotating vortex cells, u = cos(x) sin(y) sin(z),
v = -sin(x) cos(y) sin(z), w = 0. It has no analytic
solution once nonlinear vortex stretching kicks in, so it is used as a canonical
benchmark for testing CFD codes and studying the transition from smooth, ordered
flow into three-dimensional turbulence.
The Taylor-Green vortex is still used today to benchmark supercomputer CFD solvers — it is smooth and simple enough to start from an exact formula, yet rich enough to develop full 3D turbulence and a genuine turbulent kinetic-energy cascade.
A cube of tracer particles seeded in the classic Taylor-Green vortex pattern — a periodic array of counter-rotating swirls — advected in real time so you can watch it stretch, tangle and decay under adjustable Reynolds number.
The Taylor-Green initial condition decays exponentially through viscosity, but at higher Reynolds number nonlinear vortex stretching first amplifies small-scale motion into a genuine turbulent breakdown before viscosity finally wins.
Raise the Reynolds number to push the flow from clean laminar decay toward turbulent breakdown, speed up simulated time to see the full life cycle faster, and toggle the vortex-cell grid or tracer count to taste.
The Taylor-Green vortex is a standard benchmark for supercomputer CFD solvers precisely because it starts from one clean formula yet still develops a full three-dimensional turbulent energy cascade.