Stokes number

The Womersley number is also equal to the square root of the Stokes number.

Smaller Stokes numbers represent better tracing accuracy; for , particles will detach from a flow especially where the flow decelerates abruptly.

The Stokes number, , named after George Gabriel Stokes, is a dimensionless number corresponding to the behavior of particles suspended in a fluid flow.

Particles (particularly those with Stokes number close to 1) are known to accumulate in regions of high shear and low vorticity (such as turbulent boundary layers), and the mechanisms behind this phenomenon are not well understood.

Particles with low Stokes number follow fluid streamlines (perfect advection) whereas for large Stokes number, the particle's inertia dominates so that the particle will continue along its initial trajectory.

The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics (the degree to which the particles faithfully follow the flow is represented by the Stokes number).

In experimental fluid dynamics, the Stokes number is a measure of flow tracer fidelity in particle image velocimetry (PIV) experiments where very small particles are entrained in turbulent flows and optically observed to determine the speed and direction of fluid movement (also known as the velocity field of the fluid).