Nonautonomous analysis of steady Korteweg-de Vries waves under nonlocalised forcing

被引：8

作者：

Balasuriya, Sanjeeva ^{[1
]}

Binder, Benjamin J. ^{[1
]}

机构：

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2014年 / 285卷

基金：

澳大利亚研究理事会;

关键词：

Nonautonomous dynamical systems; Homoclinic trajectories; KdV equation; Free-surface flow; Solitary waves; FREE-SURFACE FLOW; CHAOTIC BEHAVIOR; SOLITARY WAVES; WATER-WAVES; EQUATION; KDV; DICHOTOMIES; MANIFOLDS; SOLITONS; TIME;

D O I：

10.1016/j.physd.2014.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently developed nonautonomous dynamical systems theory is applied to quantify the effect of bottom topography variation on steady surface waves governed by the Korteweg-de Vries (KdV) equation. Arbitrary (but small) nonlocalised bottom topographies are amenable to this method. Two classes of free surface solutions - hyperbolic and homoclinic solutions of the associated augmented dynamical system - are characterised. The first of these corresponds to near-uniform free-surface flows for which explicit formula are developed for a range of topographies. The second corresponds to solitary waves on the free surface, and a method for determining their number is developed. Formula for the shape of these solitary waves are also obtained. Theoretical free-surface profiles are verified using numerical KdV solutions, and excellent agreement is obtained. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：28 / 41

页数：14

共 58 条

[1] ON THE EXCITATION OF LONG NONLINEAR WATER-WAVES BY A MOVING PRESSURE DISTRIBUTION [J].

AKYLAS, TR .

JOURNAL OF FLUID MECHANICS, 1984, 141 (APR) :455-466

[2]

[Anonymous], 1992, Chaotic Transport in Dynamical Systems

[3] Approach for maximizing chaotic mixing in microfluidic devices [J].

Balasuriya, S .

PHYSICS OF FLUIDS, 2005, 17 (11) :1-4

[4] Direct chaotic flux quantification in perturbed planar flows: General time-periodicity [J].

Balasuriya, S .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2005, 4 (02) :282-311

[5] Optimal perturbation for enhanced chaotic transport [J].

Balasuriya, S .

PHYSICA D-NONLINEAR PHENOMENA, 2005, 202 (3-4) :155-176

[6] Cross-separatrix flux in time-aperiodic and time-impulsive flows [J].

Balasuriya, Sanjeeva .

NONLINEARITY, 2006, 19 (12) :2775-2795

[7] Chapter 1 Nonautonomous Flows as Open Dynamical Systems: Characterising Escape Rates and Time-Varying Boundaries [J].

Balasuriya, Sanjeeva .

ERGODIC THEORY, OPEN DYNAMICS, AND COHERENT STRUCTURES, 2014, 70 :1-30

[8] Nonautonomous control of stable and unstable manifolds in two-dimensional flows [J].

Balasuriya, Sanjeeva ;

Padberg-Gehle, Kathrin .

PHYSICA D-NONLINEAR PHENOMENA, 2014, 276 :48-60

[9] CONTROLLING THE UNSTEADY ANALOGUE OF SADDLE STAGNATION POINTS [J].

Balasuriya, Sanjeeva ;

Padberg-Gehle, Kathrin .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2013, 73 (02) :1038-1057

[10] Explicit invariant manifolds and specialised trajectories in a class of unsteady flows [J].

Balasuriya, Sanjeeva .

PHYSICS OF FLUIDS, 2012, 24 (12)

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