Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T22:20:50.082Z Has data issue: false hasContentIssue false
  • English
  • Français

Resonant generation of finite-amplitude waves by the uniform flow of a uniformly rotating fluid past an obstacle

Published online by Cambridge University Press:  26 February 2010

R. Grimshaw  and
Z. Yi
R. Grimshaw
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic. 3168, Australia.
Z. Yi
Affiliation:
National Research Centre for Marine Environment, Forecasts, Hai Dian Division, Beijing, China.
Get access

Abstract

In a previous paper (Grimshaw, 1990a) we showed that the resonant, or critical, flow of a rotating fluid past an axisymmetric obstacle placed on the axis of a cylindrical tube is described by a forced Korteweg-de Vries equation for the amplitude of the dominant resonant mode. Here we show that in the anomalous but important case when the oncoming flow is uniform with uniform angular velocity a different theory is required which leads to an evolution equation describing finite-amplitude waves. Some numerical solutions of this equation are described.

Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993 , pp. 30 - 50
Copyright
Copyright © University College London 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Grimshaw, R.. 1990a. Resonant flow of a rotating fluid past an obstacle: the general case. Stud. Appl. Math., 83, 249–269.CrossRefGoogle Scholar
Grimshaw, R.. 1990b. Resonant flow over Topography. In Nonlinear Evolution Equations and Dynamical Systems, Res. Rep. in Physics, ed. Carillo, S. and Ragnisco, D. (Springer, 1990), 209–211.CrossRefGoogle Scholar
Grimshaw, R.. 1992. Resonant forcing of nonlinear dispersive waves. In the Conference Proceedings, Nonlinear Dispersive Wave Systems, ed. Debnath, L. (World Scientific), 1–11.Google Scholar
Grimshaw, R. and Smyth, N.. 1986. Resonant flow of a stratified fluid over topography. J. Fluid Mech., 169, 429–464.CrossRefGoogle Scholar
Grimshaw, R. and Zengxin, Yi. 1991. Resonant generation of finite amplitude waves by the flow of a uniformly stratified fluid over topography. J. Fluid Mech., 229, 603–628.CrossRefGoogle Scholar
Grimshaw, R. and Zengxin, Yi. 1992. Resonant generation of finite-amplitude waves by flow past topography on a β- plane. Stud. Appl. Math., 88, 89–112.CrossRefGoogle Scholar
Hanazaki, H.. 1991. Upstream-advancing nonlinear waves in an axisymmetric resonant flow of rotating fluid past an obstacle. Phys. Fluids, 3A, 3117–3120.CrossRefGoogle Scholar
Leibovich, S. and Kribus, A.. 1990. Large-amplitude wavetrains and solitary waves in vortices. J. Fluid Mech., 216, 459–504.CrossRefGoogle Scholar
Leibovich, S.. 1978. The structure of vortex breakdown. Ann. Rev. Fluid Mech., 10, 221–246.CrossRefGoogle Scholar
Randall, J. D. and Leibovich, S.. 1973. The critical state: a trapped wave model of vortex breakdown. J. Fluid Mech., 58, 495–515.CrossRefGoogle Scholar
Warn, T.. 1983. The evolution of finite amplitude solitary Rossby waves on a weak shear. Stud. Appl. Math., 69, 117–133.CrossRefGoogle Scholar
Zengxin, Yi and Warn, T.. 1987. A numerical method for solving the evolution equation of solitary Rossby waves on a weak shear. Adv. Atmos. Sci., 4, 43–54.CrossRefGoogle Scholar