Leriche, E.Labrosse, G.2019-08-232019-08-232019-08-23200710.1007/s00162-006-0037-7https://infoscience.epfl.ch/handle/20.500.14299/160433WOS:0002425135000019729The unsteady dynamics of the Stokes flows, where ∇⃗ 2(𝑝𝜌)=0, is shown to verify the vector potential–vorticity ( 𝜓⃗ ,𝜔⃗ ) correlation ∂𝜓⃗ ∂𝑡+𝜈𝜔⃗ +Π⃗ =0, where the field Π⃗ is the pressure-gradient vector potential defined by ∇⃗ (𝑝𝜌)=∇⃗ ×Π⃗ . This correlation is analyzed for the Stokes eigenmodes, ∂𝜓⃗ ∂𝑡=𝜆𝜓⃗ , subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity, 𝜈(𝜔⃗ −𝜔⃗ 0)=−𝜆𝜓⃗ , where 𝜔⃗ 0 is a constant offset field, possibly zero.text::journal::journal article::research article