Tri-periodic fully three-dimensional analytic solutions for the Navier–Stokes equations. (10th May 2020)

• Record Type: Journal Article
• Authors: Antuono, Matteo
• Is Part Of: Journal of fluid mechanics. Volume 890(2020)
• Publication Date: 2020-05-10
• Subjects: Navier–Stokes equations, -- vortex dynamics, -- turbulent transition; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.126
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : 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.