# A mathematical consideration of vortex thinning in 2D turbulence

@article{Yoneda2016AMC, title={A mathematical consideration of vortex thinning in 2D turbulence}, author={Tsuyoshi Yoneda}, journal={arXiv: Analysis of PDEs}, year={2016} }

In two dimensional turbulence, vortex thinning process is one of the attractive mechanism to explain inverse energy cascade in terms of vortex dynamics. By direct numerical simulation to the two-dimensional Navier-Stokes equations with small-scale forcing and large-scale damping, Xiao-Wan-Chen-Eyink (2009) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. The aim of this paper is to analyze the vortex-thinning mechanism mathematically (using the… Expand

#### References

SHOWING 1-10 OF 22 REFERENCES

Selective decay and coherent vortices in two-dimensional incompressible turbulence.

- Physics, Medicine
- Physical review letters
- 1991

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time,… Expand

Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation

- Physics
- Journal of Fluid Mechanics
- 2009

We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale… Expand

Vorticity and Incompressible Flow: Index

- Physics
- 2001

This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. Although the… Expand

Maximum Palinstrophy Growth in 2D Incompressible Flows: Instantaneous Case

- Physics
- 2013

In this study we investigate the vortex structures which lead to the maximum possible growth of palinstrophy in two-dimensional incompressible flows on a periodic domain. It is shown that these… Expand

Small scale creation for solutions of the incompressible two dimensional Euler equation

- Mathematics
- 2013

We construct an initial data for two-dimensional Euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times. This estimate is known to be… Expand

Exponential growth of the vorticity gradient for the Euler equation on the torus

- Mathematics
- 2013

We prove that there are solutions to the Euler equation on the torus with $C^{1,\alpha}$ vorticity and smooth except at one point such that the vorticity gradient grows in $L^\infty$ at least… Expand

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… Expand

Perfect Incompressible Fluids

- Mathematics
- 1998

Introduction 1. Presentation of the equations 2. Littlewood-Paley theory 3. Around Biot-Savart's law 4. The case of a smooth initial data 5. When the vorticity is bounded 6. Vortex sheets 7. The wave… Expand

An Eulerian-Lagrangian approach for incompressible fluids: Local theory

- Physics, Mathematics
- 2000

We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial… Expand

The existence and uniqueness of nonstationary ideal incompressible flow in bounded domains in

- Mathematics
- 1973

It is shown here that the mixed initial-boundary value problem for the Euler equations for ideal flow in bounded domains of R3 has a unique solution for a small time interval. The existence of a… Expand