The Lagrangian mean flow of broadband wave fields

Currents modulate the geometry, kinematics, and dynamics of deep-water surface gravity waves. The inverse problem – inferring information about the underlying currents from measurements of the wave field – is a central question for remote sensing instruments such as scatterometers, which measure the Doppler shifted wave frequencies to infer the underlying currents. Notably, these methods do not account for the resonant interaction between long and short waves. This is a potential source of error, as the suborbital scatterometers mentioned above mostly measure shorter surface gravity waves, which are modified through nonlinear interactions with longer waves. This nonlinear interaction affects both the frequency of these waves, which is directly measured by the scatterometer, as well as their Stokes Drift, which is necessary to compute the Eulerian velocity field.

Here, we connect the phase correction for long wave - short wave interactions with the associated modification of the Lagrangian mean flow following the procedure developed for monochromatic waves by Pizzo et al. (2023). We will present novel laboratory and numerical experiments, hinting at the increased near surface drift due to these interactions currently not accounted for in standard methods that infer Stokes Drift from surface wave spectra.