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

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 p hase 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 motio n near the topography to period ir, in which n upstream-advancing waves are generated in period T. These regions extend and shift to larger T as the a verage value or amplitude of the variation of U increases. Furthermore, whe n the entrainment occurs, the spatial region where time-periodic evolution is almost attained extends toward both upstream and downstream directions w ith increasing time. (C) 2000 The Japan Society of Fluid Mechanics and Else vier Science B.V. All rights reserved.