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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 © 2010 The Author(s).link_to_subscribed_fulltex

A New Lagrangian Asymptotic Solution for Gravity–Capillary Waves in Water of Finite Depth