缓变的任意截面渠道中的孤立波

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

The Solitary Waves in a Gradually Varying Channel of Arbitrary Cross-section

摘要: 本文研究了在流动方向可以有缓慢变化的任意截面渠道中的孤立波,导出了缓变系数KdV方程,并求出了此方程的首项近似解,导出了孤立波的速度的表示式,以及孤立波的波幅与渠道几何尺寸的关系,并把它们应用于三角形渠道、矩形渠道,对于变深度、变宽度矩形渠道的情况,本文的结果与Johnson、Shuto及Mile等人所得的结果一致.

Abstract: In this paper, the solitary waves in an arbitrary cross-section channel which gradually changes in the streamwise have been studied. The KdV equation with slowly varying coefficients is derived. Thus, we produced the first term of its asymptotic solution, travel speed of solitary waves and the relation between the amplitude of wave and the geometric size of channel. The results have been applied to the cases of triangular and rectangular channels. For the channel with varying depths and breadths they are fairly consistent with those of Johnson, Shuto and Mile.

[1]	Grimshaw,R.,The solitary waves in water of variable depth.J.Fluid Mech.42,(1970) 639-656.
[2]	Grimshaw,R.,Long nonlinear internal waves in channels of arbitrary cross-section.J.Fluid Mech.86,(1978),415-431.
[3]	Johnson,R.S.,On the development of a solitary wave moving over an uneven bottom.Proc.Camb.Phil.Soc.73,(1973a),183-203.
[4]	Johnson,R.S.,On an asymptotic solution of the Korteweg-de Vries equation with slowly varying coefficients,J.Fluid Mech.60,(1973b),813-824.
[5]	Lamb,H.,Hydrodynamics,Cambridge University Press.(1932).
[6]	Mile,John W.,Note on a solitary wave in a slowly varying channel,J.Fluid Mech.80,(1977),149-152.
[7]	Mile,John W.,Solitary Waves,Annual Rev.Fluid Mech.12,(1980) 10-43.
[8]	Peregrine,D.H.,Long waves in a uniform channel of arbitrary cross-section,J.Fluid Mech. 32,(1968),353-365.
[9]	Peter,A.S.,Rotational and irrotational solitary waves in a channel with arbitrary crosssection,Comm.Pure and Appl.Math.19,No.4,(1966),445.
[10]	Shuto,N.,Nonlinear long waves in a channel of variable section,Coastal Engin.in Japan. 17,(1974),1-12.