A Lagrangian approach to the weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow

被引：0

作者：

Fukumoto, Yasuhide ^{[1
]}

Mie, Youichi ^{[2
]}

机构：

[1] Kyushu Univ, Inst Math Ind, Nishi Ku, Fukuoka 8190395, Japan

[2] Sumitomo Rubber Ind Ltd, Chuo Ku, Kobe, Hyogo 6510071, Japan

来源：

FLUID DYNAMICS RESEARCH | 2015年 / 47卷 / 01期

基金：

日本学术振兴会;

关键词：

Kelvin wave; mean flow; Lagrangian approach; weakly nonlinear instability; secondary instability; STRAIGHT VORTEX FILAMENT; LAMB-OSEEN VORTEX; ELLIPTIC INSTABILITY; FIELD; REDUCTION; STABILITY; BREAKDOWN; CYLINDER; LIE;

D O I：

10.1088/0169-5983/47/1/015509

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We develop a general framework of using the Lagrangian variables for calculating the energy of waves on a steady Euler flow and the mean flow induced by their nonlinear interaction. With the mean flow at hand we can determine, without ambiguity, all the coefficients of the amplitude equations to third order in amplitude for a rotating flow subject to a steady perturbation breaking the circular symmetry of the streamlines. Moreover, a resonant triad of waves is identified which brings in the secondary instability of the MooreSaffman- Tsai-Widnall instability, and with the aid of the energetic viewpoint, resonant amplification of the waves without bound is numerically confirmed.

引用

页码：1 / 14

页数：14