# A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations

@article{Jeong2019ARO, title={A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations}, author={In-Jee Jeong and Tsuyoshi Yoneda}, journal={arXiv: Analysis of PDEs}, year={2019} }

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the 3D incompressible Euler equations, and show that such behavior induces energy cascade in the absence of nonlinear scale-interaction. From…

## One Citation

On Singular Vortex Patches, I: Well-posedness Issues

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The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show…

## References

SHOWING 1-10 OF 25 REFERENCES

An Onsager singularity theorem for Leray solutions of incompressible Navier–Stokes

- MathematicsNonlinearity
- 2019

We study in the inviscid limit the global energy dissipation of Leray solutions of incompressible Navier–Stokes on the torus , assuming that the solutions have norms for Besov space that are bounded…

Homogeneous solutions to the 3D Euler system

- Mathematics
- 2015

We study stationary homogeneous solutions to the 3D Euler equation. The problem is motivated be recent exclusions of self-similar blowup for Euler and its relation to Onsager conjecture and…

2D Homogeneous Solutions to the Euler Equation

- Mathematics
- 2014

In this paper we study classification of homogeneous solutions to the stationary Euler equation with locally finite energy. Written in the form u = ∇⊥Ψ, Ψ(r, θ) = r λψ(θ), for λ > 0, we show that…

On the energy spectrum for weak solutions of the Navier–Stokes equations

- Mathematics, Physics
- 2005

We consider the decay at high wavenumbers of the energy spectrum for weak solutions to the three-dimensional forced Navier–Stokes equation in the whole space. We observe that known regularity…

Swirl Condition in Low-Pressure Vortices

- Physics
- 1998

A numerical method of extraction of the axis of tubular vortices in turbulent flows, which was previously proposed by Miura and Kida [J. Phys. Soc. Jpn. 66 (1997)], is improved by imposing a swirl…

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

- PhysicsJ. Nonlinear Sci.
- 2019

It is proved that for weak solutions of the Euler equations, the Lagrangian forward/backward dispersion measure matches onto the energy defect (Onsager in Nuovo Cimento (Supplemento) 6:279–287, 1949) and that a similar connection holds for time asymmetry of Richardson two-particle dispersion and cascade direction.

Ill-posedness for the Incompressible Euler Equations in Critical Sobolev Spaces

- Mathematics
- 2016

For the 2D Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong…

Remarks on the breakdown of smooth solutions for the 3-D Euler equations

- Mathematics
- 1984

The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations. In other words, if a solution of the Euler equations is initially…

Multi-scale gradient expansion of the turbulent stress tensor

- PhysicsJournal of Fluid Mechanics
- 2006

Turbulent stress is the fundamental quantity in the filtered equation for large-scale velocity that reflects its interactions with small-scale velocity modes. We develop an expansion of the turbulent…

Ill-posedness results in critical spaces for some equations arising in hydrodynamics

- Mathematics
- 2014

Many questions related to well-posedness/ill-posedness in critical spaces for hydrodynamic equations have been open for many years. In this article we give a new approach to studying norm inflation…