A mathematical consideration of vortex thinning in 2D turbulence
Abstract
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 twodimensional NavierStokes equations with smallscale forcing and largescale damping, XiaoWanChenEyink (2009) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. The aim of this paper is to analyze the vortexthinning mechanism mathematically (using the incompressible Euler equations), and give a mathematical evidence that largescale vorticity gains energy from smallscale vorticity due to the vortexthinning process.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.00107
 Bibcode:
 2016arXiv160900107Y
 Keywords:

 Mathematics  Analysis of PDEs;
 Physics  Fluid Dynamics