Vector Potential - Vorticity correlation and corner behaviors from the Stokes eigenmodes in square and cube

Abstract

A first deep insight of the Stokes eigenmodes in the fully confined domain (square and cubical) is reported. First, the dynamics of the Stokes eigenmodes flows is established leading to a collinear relationship between the vector potential and the vorticity. Secondly, from the analysis of the corner eddies made by Moffatt, the existence of corner vortices in a fully confined trihedral rectangular corner is reported when numerically computing the Stokes eigenmodes in the cube. A first analysis in term of types, sequence, and flow structures is provided.