What you are looking at
A steady stream of fluid flows from left to right past a fixed circular cylinder. The drifting dots are
tracer particles carried along by the flow — their trails reveal the streamlines.
Whether the flow stays smooth or breaks up depends on a tug-of-war between two effects: the fluid's
inertia (which wants to keep moving and tumble) and its
viscosity
(internal friction, which wants to smooth everything out).
Viscosity
Viscosity is a fluid's resistance to flowing — honey is very viscous, water much less so, air less still.
It arises because neighbouring layers of fluid moving at different speeds drag on one another. Newton's law
of viscosity captures this shear stress:
τ = μ (dv/dy)
where μ is the viscosity and dv/dy is the velocity gradient between layers. Turn the viscosity up in the
simulation and the fluid moves in orderly, parallel sheets —
laminar flow.
The Reynolds number
The single number that decides the character of the flow is the dimensionless
Reynolds number:
Re = ρ v D / μ = (inertial forces) / (viscous forces)
with ρ the density, v the speed, D the cylinder diameter and μ the viscosity.
Low Re
(thick fluid, slow flow, small body) means viscosity dominates and the flow is smooth and laminar.
High Re means inertia wins and the flow becomes unsteady and chaotic —
turbulent. Because v and D are on top and μ is on the bottom, you can reach the same Re by
speeding up the flow, shrinking the viscosity, or growing the cylinder.
The story as Re climbs
Re < 5: creeping (Stokes) flow — the streamlines slip around the cylinder almost
symmetrically.
Re ≈ 5–40: two steady eddies sit attached behind the cylinder.
Re ≈ 40–1000: those eddies peel off alternately, top then bottom, forming the beautiful
von Kármán vortex street — the same effect that makes flags flutter and power lines hum.
The shedding frequency follows the
Strouhal relation f = St·v/D with St ≈ 0.2.
Re > ~2000: the wake becomes fully
turbulent, a churning mess of
eddies on every scale.
Things to try
Start with high viscosity and watch the smooth laminar flow, then lower it step by step to trigger the
vortex street and finally turbulence — the Reynolds readout and regime label track the transition. Speed
the flow up for the same effect, or grow the cylinder. Use the slow-motion button to watch individual
vortices peel away from the cylinder one at a time.