Stokes boundary layer

In fluid dynamics, the Stokes boundary layer, or oscillatory boundary layer, refers to the boundary layer close to a solid wall in oscillatory flow of a viscous fluid. Or, it refers to the similar case of an oscillating plate in a viscous fluid at rest, with the oscillation direction(s) parallel to the plate. For the case of laminar flow at low Reynolds numbers over a smooth solid wall, George Gabriel Stokes – after whom this boundary layer is called – derived an analytic solution, one of the few exact solutions for the Navier–Stokes equations. In turbulent flow, this is still named a Stokes boundary layer, but now one has to rely on experiments, numerical simulations or approximate methods in order to obtain useful information on the flow.

The thickness of the oscillatory boundary layer is called the Stokes boundary-layer thickness.

An important observation from Stokes' solution for the oscillating Stokes flow is, that vorticity oscillations are confined to a thin boundary layer and damp exponentially when moving away from the wall. This observation is also valid for the case of a turbulent boundary layer. Outside the Stokes boundary layer – which is often the bulk of the fluid volume – the vorticity oscillations may be neglected. To good approximation, the flow velocity oscillations are irrotational outside the boundary layer, and potential flow theory can be applied to the oscillatory part of the motion. This significantly simplifies the solution of these flow problems, and is often applied in the irrotational flow regions of sound waves and water waves.

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