Corpus ID: 119171937

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}
}
  • T. Yoneda
  • Published 1 September 2016
  • Physics, Mathematics
  • arXiv: Analysis of PDEs
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.
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
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-scaleExpand
Vorticity and Incompressible Flow: Index
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 theExpand
Maximum Palinstrophy Growth in 2D Incompressible Flows: Instantaneous Case
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 theseExpand
Small scale creation for solutions of the incompressible two dimensional Euler equation
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 beExpand
Exponential growth of the vorticity gradient for the Euler equation on the torus
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 leastExpand
Ill-posedness for the Incompressible Euler Equations in Critical Sobolev Spaces
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 belongExpand
Perfect Incompressible Fluids
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 waveExpand
An Eulerian-Lagrangian approach for incompressible fluids: Local theory
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 partialExpand
The existence and uniqueness of nonstationary ideal incompressible flow in bounded domains in
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 aExpand
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