This Lagrangian drift of the fluid parcels is known as the Stokes drift.

For instance, a particle floating at the free surface of water waves, experiences a net Stokes drift velocity in the direction of wave propagation.

The Stokes drift was formulated for water waves by George Gabriel Stokes in 1847.

As derived below, the horizontal component ū(z) of the Stokes drift velocity for deep-water waves is approximately:

The Stokes drift velocity , which is the particle drift after one wave cycle divided by the period, can be estimated using the results of linear theory:

In fluid dynamics, the Coriolis-Stokes force is a force in a rotating fluid due to interaction of the Coriolis effect and wave induced Stokes drift.

For a pure wave motion in fluid dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow.

The Stokes drift is the difference in end positions, after a predefined amount of time (usually one wave period), as derived from a description in the Lagrangian and Eulerian coordinates.

As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.

However, for nonlinear waves, particles exhibit a Stokes drift for which a second-order expression can be derived from the results of Airy wave theory (see the table above on second-order wave properties).

More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel, and the average Eulerian flow velocity of the fluid at a fixed position.

The specification of mean properties for the oscillatory part of the flow, like: Stokes drift, wave action, pseudomomentum and pseudoenergy - and the associated conservation laws - arises naturally when using the GLM method.

But also in the Eulerian frame of reference the notion of fluid parcels can be advantageous, for instance in defining the material derivative, streamlines, streaklines, and pathlines; or for determining the Stokes drift.