Whether flow past an obstacle stays smooth or breaks into a swirling wake depends on a single dimensionless number: the ratio of inertial to viscous forces.
Re = U·D / ν (flow speed × diameter / kinematic viscosity)
Re < ~5 attached, laminar
Re ~ 40-200 steady vortex pair, then periodic shedding begins
Re > ~200 Kármán vortex street — alternating vortices peel off
St = f·D / U (Strouhal number, ≈0.2 in the shedding regime)
- Flow speed — raises Re, the main driver of the transition to shedding.
- Cylinder diameter — a bigger obstacle disturbs more flow, also raising Re.
- Viscosity — thicker (more viscous) fluid damps out vortices, lowering Re and calming the wake.
Real-world relevance: this exact vortex shedding is what makes suspension-bridge decks and smokestacks need aerodynamic damping — the Tacoma Narrows Bridge collapse in 1940 was driven by resonance with vortex-induced oscillation.