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Vector potential-vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain

Leriche, E. ; Labrosse, G.

In: Theoretical and Computational Fluid Dynamics, 2007, vol. 21, no. 1, p. 1-13

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    Titre
    • Vector potential-vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain
    Auteur
    • Leriche, E.. Laboratoire d'Ingénierie Numérique, Institut des Sciences de l'Energie, Faculté des Sciences et Techniques de l'Ingénieur, Ecole Polytechnique Fédérale de Lausanne, Station 9, 1015, Ecublens, Switzerland
    • Labrosse, G.. Department of Chemical Engineering, University of Florida 227 ChE, PO Box 116005, 32611, Gainesville, FL, USA
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Theoretical and Computational Fluid Dynamics, 2007, vol. 21, no. 1, p. 1-13. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:321425
    Summary
    The unsteady dynamics of the Stokes flows, where $$\vec{\nabla}^{2} \left(\frac{p}{\rho}\right) =0$$ , is shown to verify the vector potential-vorticity ( $$\vec{\psi},\,\vec{\omega}$$ ) correlation $$\frac{\partial\vec{\psi}}{\partial t}+\nu\,\vec{\omega}+\vec{\Pi}=0$$ , where the field $$\vec{\Pi}$$ is the pressure-gradient vector potential defined by $$\vec{\nabla} \left(\frac{p}{\rho}\right)=\vec{\nabla}\times\vec{\Pi}$$ . This correlation is analyzed for the Stokes eigenmodes, $$\frac{\partial\vec{\psi}}{\partial t}=\lambda\,\vec{\psi}$$ , 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, $$\nu\,\left(\vec{\omega}-\vec{\omega}_0\right)=-\lambda\,\vec{\psi}$$ , where $$\vec{\omega}_0$$ is a constant offset field, possibly zero