Steady water waves with a critical layer

被引：138
作者：
Wahlen, Erik [1 ]
机构：
[1] Lund Univ, Ctr Math Sci, S-22100 Lund, Sweden
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 06期
关键词：
PARTICLE TRAJECTORIES; ARBITRARY DISTRIBUTION; PERIODIC CAPILLARY; VORTICITY; UNIQUENESS; BIFURCATION; SYMMETRY; STOKES; FLOWS;
D O I：
10.1016/j.jde.2008.10.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct small-amplitude steady periodic water waves with constant vorticity. Among these are certain waves with the property that in a frame moving with the wave there is a 'critical layer' with closed streamlines in the fluid. These waves, which do not exist in the irrotational setting, are studied in detail. In particular we give a full description of the particle paths. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：2468 / 2483
页数：16
相关论文
共 41 条
[1]  
BENNEY DJ, 1969, STUD APPL MATH, V48, P181
[2]   Secondary criticality of water waves. Part 1. Definition, bifurcation and solitary waves [J].
Bridges, T. J. ;
Donaldson, N. M. .
JOURNAL OF FLUID MECHANICS, 2006, 565 :381-417
[3]  
Buffoni B., 2003, PRINCETON SER APPL M, DOI 10.1515/9781400884339
[4]   Variational formulations for steady water waves with vorticity [J].
Constantin, A ;
Sattinger, D ;
Strauss, W .
JOURNAL OF FLUID MECHANICS, 2006, 548 (151-163) :151-163
[5]   Particle trajectories in linear water waves [J].
Constantin, Adrian ;
Villari, Gabriele .
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2008, 10 (01) :1-18
[6]   Particle trajectories in linear deep-water waves [J].
Constantin, Adrian ;
Ehrnstrom, Mats ;
Villari, Gabriele .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (04) :1336-1344
[7]   Symmetry of steady periodic gravity water waves with vorticity [J].
Constantin, Adrian ;
Ehrnstrom, Mats ;
Wahlen, Erik .
DUKE MATHEMATICAL JOURNAL, 2007, 140 (03) :591-603
[8]   Stability properties of steady water waves with vorticity [J].
Constantin, Adrian ;
Strauss, Walter A. .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2007, 60 (06) :911-950
[9]   The trajectories of particles in Stokes waves [J].
Constantin, Adrian .
INVENTIONES MATHEMATICAE, 2006, 166 (03) :523-535
[10]  
Crandall M.G., 1971, J FUNCT ANAL, V8, P321
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