Flow over a circular cylinder

A cylinder in a steady stream sheds vortices alternately from each side. Below about Re = 47 it does not shed at all; above it, the wake becomes a periodic street with a frequency that depends only on the Reynolds number.

This is the only case here with no steady answer. Everything else on this site reaches a steady state and is compared field against field. Here the answer is a frequency, and getting it requires the unsteady solver, the time scheme and the force integration all to be right at once. A code can produce a beautiful steady wake and be completely wrong about this.

Roshko’s equation (2a) gives St = 0.212 (1 − 21.2/Re) over 50 < Re < 150, which brackets all three cases here. It is an empirical fit, not an exact solution, and Roshko states the scatter of his own measurements about it as 4 %.

That is the floor on what agreement can mean. A computed Strouhal number inside 4 % has matched the correlation as closely as the correlation matches the data behind it. Comparing against it is validation, not verification.

Every point is inside Roshko’s own 4 % scatter, and the three sit on a curve of the right shape — St rising with Re, tracking the fit rather than crossing it.

Re-measured on 27 August 2026 on a genuinely two-dimensional mesh — one cell thick, with the thin faces an empty pair rather than the roughly eight-cell slab the earlier figures were measured on.

No prism layers, and that is not a shortcut. The layer thickness is sized from a turbulent flat-plate correlation, which asks for 2.792 m of boundary layer on a 1 m cylinder at Re = 100 — four decades outside the correlation’s range. snappyHexMesh attempts the extrusion, the quality floor rejects it, and the removal leaves inside-out cells that diverge the pressure solve on its first iteration. A laminar cylinder has no log layer to resolve, so the layers are switched off.

Domain extent and blockage are recorded because they change the answer. The published data are for effectively unbounded flow. A cylinder in a narrow domain sheds at a measurably different frequency, and that is not a solver error — it is a different problem. It is the most common reason a cylinder case “fails” validation.