Asymptotic Solutions of the Navier-Stokes Equations and Systems of Stretched Vortices Filling a Three-Dimensional Volume

被引：1

作者：

Maslov, V. P. ^{[1
]}

Shafarevich, A. I. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 91卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

Navier-Stokes equation; vortex system; stretched vortex; vortex filament; Euler equation; divergence-free vector field; Reynolds equation; Reynolds stress; BOUNDARY-LAYER; VORTEX RINGS; DISTRIBUTIONS; VICINITY; LAW;

D O I：

10.1134/S0001434612010221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct asymptotic solutions of the Navier-Stokes equations describing periodic systems of vortex filaments entirely filling a three-dimensional volume. Such solutions are related to certain topological invariants of divergence-free vector fields on the two-dimensional torus. The equations describing the evolution of of such a structure are defined on a graph which is the set of trajectories of a divergence-free field.

引用

页码：207 / 216

页数：10