_ Vol. 26 (5) (2000) pp. 289-304 _
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Fluid Dynamics Research, Vol. 26 (5) (2000) pp. 289-304
© 2000 The Japan Society of Fluid Mechanics. Published by Elsevier Science B.V. All rights reserved.
PII: S0169-5983(99)00027-1

Generation of long waves in a fluid flowing over a localized topography at a periodically varying velocity

Yasuo Ohsugi a and Mitsuaki Funakoshi b * mitsu@acs.i.kyoto-u.ac.jp

a Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, Yoshida-Honmachi, Kyoto, 606-8501, Japan
b Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto, 606-8501, Japan

Received 23 March 1999; received in revised form 27 May 1999; accepted 23 June 1999

Abstract

The generation of long waves in a fluid flowing over a localized topography is examined numerically using the forced KdV equation under the assumption that the velocity U of the fluid far from the topography is close to the phase speed of a linear long wave and varies periodically with period T. For T within a few regions, we observe the 1:n entrainment of the wave motion near the topography to period T, in which n upstream-advancing waves are generated in period T. These regions extend and shift to larger T as the average value or amplitude of the variation of U increases. Furthermore, when the entrainment occurs, the spatial region where time-periodic evolution is almost attained extends toward both upstream and downstream directions with increasing time.

PACS: 47.35.+i; 92.10.Hm

Keywords: Forced KdV equation; Periodic flow; Entrainment; Localized topography

*Corresponding author. Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto, 606-8501, Japan. Fax: +81-75-753-4923.

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