Potential flows of incompressible fluids with constant properties are irrotational solutions of the Navier–Stokes equations that satisfy Laplace's equation. How do these solutions enter into the general problem of viscous fluid mechanics? Under certain conditions, the Helmholtz decomposition says that solutions of the Navier–Stokes equations can be decomposed into a rotational part and an irrotational part satisfying Laplace's equation. The irrotational part is required for satisfying the boundary conditions; in general, the boundary conditions cannot be satisfied by the rotational velocity, and they cannot be satisfied by the irrotational velocity; the rotational and irrotational velocities are both required and they are tightly coupled at the boundary. For example, the no-slip condition for Stokes flow over a sphere cannot be satisfied by the rotational velocity; harmonic functions that satisfy Laplace's equation subject to a Robin boundary condition in which the irrotational normal and tangential velocities enter in equal proportions are required.

The literature that focuses on the computation of layers of vorticity in flows that are elsewhere irrotational describes boundary-layer solutions in the Helmholtz decomposed forms. These kinds of solutions require small viscosity and, in the case of gas–liquid flows, are said to give rise to weak viscous damping. It is true that viscous effects arising from these layers are weak, but the main effects of viscosity in so many of these flows are purely irrotational, and they are not weak.