On Water Waves Generated by a Bottom Obstacle Translating at a Subcritical Speed
J. Fluid Mech. (2021), vol. 923, A26, doi:10.1017/jfm.2021.537 . On water waves generated by a bottom obstacle translating at a subcritical speed Peter H.-Y. Lo1,† and Philip L.-F. Liu2,3,4 https://www.cambridge.org/core/terms 1Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei City 10617, Taiwan 2Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576, Republic of Singapore 3Institute of Hydrological and Oceanic Sciences, National Central University, Taoyuan City 320317, Taiwan 4Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA (Received 14 August 2020; revised 25 March 2021; accepted 14 June 2021) This study investigates water waves generated by a bottom obstacle translating at a subcritical speed in constant water depth, using a combination of analytical and numerical , subject to the Cambridge Core terms of use, available at approaches. The newly derived analytical solutions reveal two types of waves – the transient free waves that propagate radially outwards, and the trapped wave that stays on top of the translating bottom obstacle. Closed-form asymptotic solutions for both the free surface and the flow velocities are derived in the far field, and near the leading wave or in the shallow water limit. The far-field leading waves are mathematically shown to be insensitive to the exact shape of the obstacle. Numerical long-wave models are employed 02 Oct 2021 at 01:29:52 to examine effects unaccountable by the linear analytical solutions. Nonlinear effects are , on found to cause only small deviations from the linear solutions.
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