The role of Lagrangian drift in the geometry, kinematics and dynamics of surface waves

The role of the Lagrangian mean flow, or drift, in modulating geometry, kinematics and dynamics rotational irrotational deep-water surface gravity waves is examined. A general theory for permanent progressive on an arbitrary vertically sheared steady flow derived reference frame mapped to Eulerian frame. viewpoint offers tremendous flexibility due particle labelling freedom allows us reveal how key physical wave behaviour arises from a kinematic constraint vorticity fluid, inter alia nonlinear correction phase speed finite amplitude waves, free geometry velocity frame, connection between drift Benjamin–Feir instability. To complement illustrate our theory, small laboratory experiment demonstrates specially tailored can almost completely attenuate instability, qualitative agreement with theory. application these results problems remote sensing ocean modelling discussed. We provide answer long-standing question: techniques based observing current-induced shifts dispersion will measure Lagrangian, not Eulerian, current.