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- Title
Vector potential–vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain.
- Authors
Leriche, E.; Labrosse, G.
- Abstract
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.
- Subjects
STOKES' theorem; EIGENFUNCTIONS; ROTATIONAL motion; VECTOR fields; FERROMAGNETIC materials; MAGNETIC domain; FLUID dynamics
- Publication
Theoretical & Computational Fluid Dynamics, 2007, Vol 21, Issue 1, p1
- ISSN
0935-4964
- Publication type
Article
- DOI
10.1007/s00162-006-0037-7