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Tri-periodic fully three-dimensional analytic solutions for the Navier–Stokes equations

Published online by Cambridge University Press:  17 March 2020

Matteo Antuono Open the ORCID record for Matteo Antuono [Opens in a new window]
Matteo Antuono*
Affiliation:
CNR-INM, Via di Vallerano 139, 00128 Rome, Italy
*
†Email address for correspondence: matteo.antuono@cnr.it
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Abstract

In this paper we derive unsteady tri-periodic laminar solutions of the Navier–Stokes equations. In particular, these represent fully three-dimensional (3-D) flows, since all the velocity components depend non-trivially on all three coordinate directions. We show that they belong to the class of Beltrami flows and can be gathered in two distinct solutions characterized by positive and negative helicity. These can be regarded as an extension in three dimensions of the bi-periodic vortex solution by Taylor (Phil. Mag., vol. 46, 1923, pp. 671–674). Their use as benchmarks for checking the accuracy of 3-D numerical codes and/or studying the onset of turbulence is suggested.

JFM classification

Vortex Flows: Vortex dynamics Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A23
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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