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

@article{Antuono2020TriperiodicFT, title={Tri-periodic fully three-dimensional analytic solutions for the Navier–Stokes equations}, author={Matteo Antuono}, journal={Journal of Fluid Mechanics}, year={2020}, volume={890} }

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…

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## References

SHOWING 1-10 OF 20 REFERENCES

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

- Physics
- 2018

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This…

On the regularity of the solutions to the 3D Navier–Stokes equations: a remark on the role of the helicity

- Mathematics
- 2009

Exact fully 3D Navier–Stokes solutions for benchmarking

- Philosophy
- 1994

SUMMARY Unsteady analytical solutions to the incompressible Navier-Stokes equations are presented. They are fully three-dimensional vector solutions involving all three Cartesian velocity components,…

Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

- PhysicsPhysics of Fluids
- 2019

The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV…

Exact Solutions of the Unsteady Navier-Stokes Equations

- Mathematics
- 1989

The unsteady Navier-Stokes equations are a set of nonlinear partial differential equations with very few exact solutions. This paper attempts to classify and review the existing unsteady exact…

A note on the decay of vortices in a viscous fluid

- Mathematics, Physics
- 2011

In this short note, we extend a result due to Taylor (1923) concerning eddies in the plane flow of an incompressible Navier–Stokes fluid, each of which is rotating in the opposite sense to four of…

Small-scale structure of the Taylor–Green vortex

- Physics
- 1983

The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of…

Simulation of transition and turbulence decay in the Taylor–Green vortex

- Physics
- 2007

Conventional large-eddy simulation (LES) and monotone integrated LES (MILES) are tested in emulating the dynamics of transition to turbulence in the Taylor–Green vortex (TGV). A variety of subgrid…

Slow Viscous Flow

- Engineering
- 1995

Many of the problems already presented dealt with situations where inertia forces were cither zero (parallel flow) or could be neglected because of some peculiarities, for example, flow in thin…

Smoothed particle hydrodynamics method from a large eddy simulation perspective

- Environmental Science
- 2017

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier–Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy…