Abstract
A third-order Lagrangian asymptotic solution is derived for gravity–capillary waves in water of finite depth. The explicit parametric solution gives the trajectory of a water particle and the wave kinematics for Lagrangian points above the mean water level, and in a water column. The water particle orbits and mass transport velocity as functions of the surface tension are obtained. Some remarkable trajectories may contain one or multiple sub-loops for steep waves and large surface tension. Overall, an increase in surface tension tends to increase the motions of surface particles including the relative horizontal distance travelled by a particle as well as the time-averaged drift velocity
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The authors would like to acknowledge the insightful critiquing of the two referees.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hsu, HC., Ng, CO. & Hwung, HH. A New Lagrangian Asymptotic Solution for Gravity–Capillary Waves in Water of Finite Depth. J. Math. Fluid Mech. 14, 79–94 (2012). https://doi.org/10.1007/s00021-010-0045-7
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DOI: https://doi.org/10.1007/s00021-010-0045-7