The free surface on a liquid filling a trench heated from its side-Reference-Cited by-同舟云学术

The free surface on a liquid filling a trench heated from its side

Published:1975-06-10 Issue:3 Volume:69 Page:565-589
ISSN:0022-1120
Container-title:Journal of Fluid Mechanics
language:en
Short-container-title:J. Fluid Mech.

Author:

Joseph Daniel D.,Sturges Leroy

Abstract

In this paper we compute the motion and the shape of the free surface on a liquid in a trench heated from its side. The analysis is based on Joseph's Lagrangian theory of domain perturbations, which is developed in general and through simple examples, chosen so as to make the comparison of the Lagrangian method with Stokes's Eulerian theory very clear. The perturbation problems are resolved analytically by application of biorthogonality conditions to a powerful set of biharmonic eigenfunctions.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference15 articles.

1. Struik, D. J. 1926 Détermination rigoureuse des ondes irrotationnelles périodiques dans un canal á profondeur finie Math. Annln,95,595–634.

2. Smith, R. C. T. 1952 The bending of a semi-infinite strip Aust. J. Scie. Res. 5,227–237.

3. Sattinger, D. 1975 On the free surface of viscous fluid motion.Proc. Roy. Soc. A (to appear).

4. Joseph, D. D. 1974 Slow motion and viscometric motion. Stability and bifurcation of the rest state of a simple fluid Arch. Rat. Mech. Anal. 56,99–157.

5. Johnson, M. W. & Little, R. W. 1965 The semi-infinite elastic strip Quart. Appl. Math. 22,335.

Cited by 55 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Analytical Solution of Thermocapillary Flow in Cylindrical Annuli with Curved Free Surface;Journal of Thermal Science;2019-04-23

2. Axisymmetric shape of gas bubbles in a uniform flow: Numerical study of bifurcation by analytic continuation;Applied Mathematics and Computation;2016-02

3. Low-Reynolds-number flow through two-dimensional shunts;Journal of Fluid Mechanics;2013-04-16

4. Stokes flow in curved channels;Journal of Computational and Applied Mathematics;2006-03

5. An approximate analytic solution method for the biharmonic problem;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2006-01-17