Strouhalnumber

Strouhal number (St) is a dimensionless parameter that characterizes oscillating or unsteady flows. It relates the frequency of unsteady phenomena, such as vortex shedding, to a characteristic length and the mean flow speed. It is defined as St = fL/U, where f is the frequency of the unsteady motion, L is a representative length of the body or flow feature, and U is the flow velocity.

In practice, L is chosen to match the geometry: for a circular cylinder in crossflow, L is the diameter D; for a wing section, L could be the chord length. The Strouhal number provides a nondimensional measure that helps compare flows across scales and Reynolds numbers.

Vortex shedding from bluff bodies is a common application. For a circular cylinder, the Strouhal number is approximately 0.2 over a broad range of Reynolds numbers roughly from 100 to 10,000, though the exact value varies with Re and surface conditions. The Strouhal number is not universal; its value depends on the shape, boundary conditions, and Reynolds number of the flow.

Applications include predicting unsteady forces and vibrations in structures due to vortex shedding, scaling model tests to full size, and understanding propulsion in aquatic and avian locomotion. In biology and engineering, Strouhal numbers around 0.2–0.4 are often linked with efficient flapping propulsion, though this range is not universal.

The Strouhal number is one of several dimensionless groups used in unsteady fluid dynamics, complementing the Reynolds number and others to describe the frequency content of flows.