Exact solutions of the Navier–Stokes equations generated by the eigenfunctions of the Stokes operator

We derive a class of exact solutions to the incompressible unsteady Navier–Stokes equations. These solutions are generated by the eigenfunctions of the Stokes operator and can be applied to studying boundary value problems for the Navier–Stokes equations related to pipe and channel flows. We explore...

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Veröffentlicht in:Physics of fluids (1994) 2024-06, Vol.36 (6)
1. Verfasser: Baron, Alexander
Format: Artikel
Sprache:eng
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Zusammenfassung:We derive a class of exact solutions to the incompressible unsteady Navier–Stokes equations. These solutions are generated by the eigenfunctions of the Stokes operator and can be applied to studying boundary value problems for the Navier–Stokes equations related to pipe and channel flows. We explore the relation between the spectrum of the Stokes operator, generalized Beltrami flows, and exact solutions of the Navier–Stokes equations. Relevant properties of the Stokes eigenfunctions are also discussed in some detail.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0212146