Existence of trapped modes along periodic structures in a two-layer fluid

被引：8

作者：

Cal, F. S. ^{[1
]}

Dias, G. S. A. ^{[1
]}

Videman, J. H. ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Inst Super Tecn, Ctr Matemat & Aplicacoes, Dept Matemat, P-1049001 Lisbon, Portugal

来源：

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS | 2012年 / 65卷 / 02期

关键词：

BLOCH SURFACE-WAVES; WATER-WAVES; EDGE WAVES; GRATINGS; GUIDES;

D O I：

10.1093/qjmam/hbs001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider trapping of linear water waves by infinite arrays of three-dimensional periodic structures in a two-layer fluid. We derive a geometric condition ensuring the existence of trapped modes and give several examples of structures satisfying the condition and supporting edge waves. We also study how the layer height and density ratios affect the sufficient condition.

引用

页码：273 / 292

页数：20

共 27 条

[1] [Anonymous], 1945, Hydrodynamics
[2] [Anonymous], 1998, PARTIAL DIFFERENTIAL
[3] Birman M.S., 1987, Spectral theory of self-adjoint operators in Hilbert space
[4] Evans D. V., 1993, Q J MECH APPL MATH, V46, P644
[5] EXISTENCE THEOREMS FOR TRAPPED MODES
EVANS, DV
LEVITIN, M
VASSILIEV, D
[J]. JOURNAL OF FLUID MECHANICS, 1994, 261 : 21 - 31
[6] EDGE WAVES ALONG PERIODIC COASTLINES .2.
EVANS, DV
FERNYHOUGH, M
[J]. JOURNAL OF FLUID MECHANICS, 1995, 297 : 307 - 325
[7] Evans LC., 2018, Measure Theory and Fine Properties of Functions
[8] ON THE MOTION OF FLOATING BODIES .2. SIMPLE HARMONIC MOTIONS
JOHN, F
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1950, 3 (01) : 45 - 101
[9] Exponentially decreasing solutions of diffraction problems on a rigid periodic boundary
Kamotskii, IV
Nazarov, SA
[J]. MATHEMATICAL NOTES, 2003, 73 (1-2) : 129 - 131
[10] Wave interaction with two-dimensional bodies floating in a two-layer fluid: uniqueness and trapped modes
Kuznetsov, N
McIver, M
McIver, P
[J]. JOURNAL OF FLUID MECHANICS, 2003, 490 : 321 - 331

← 1 2 3 →