Abstract
Abstract A new base for three-dimensional divergence-free vector fields in Hilbert space (Galerkin method) is proposed. The base fields have vanishing boundary conditions for their curl and are useful to solve the incompressible Navier-Stokes equation. The base vector potentials are obtained as the eigensolutions of the squared Laplace operator. We first derive the operator in a simply connected domain and then study Couette flow in the small gap approximation. The method yields a rapidly converging critical Taylor number and in lowest approximation a three mode model for the Taylor vortices, similar to the Lorenz model. It represents the first bifurcation of the flow very well.
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