Impact of submesoscale currents on surface waves: the U2H map

Ocean turbulence at meso- and submesocales affects the propagation of surface waves through refraction and scattering. This induces spatial modulations in wave energy, with implications for air–sea exchanges, the likelihood of extreme waves, and remote sensing. We develop a theoretical framework that relates modulations in significant wave height (SWH) to the currents that induce them. We exploit the asymptotic smallness of the ratio of typical current speed to wave group speed (which holds for wavelengths above 10 m or so) to derive a linear map – the U2H map – that relates SWH anomalies to the surface current velocity. This map is a convolution, non-local in space but expressible as a product in Fourier space and, crucially, independent of the magnitude of the Fourier vector. The properties of the map show how the SWH anomaly responds differently to the vortical and divergent parts of the currents, and how the anisotropy of the wave spectrum is key to large current-induced SWH anomalies. Analysing the U2H map, in particular for swell-like, highly directional waves enables us to explain a series of earlier numerical observations. We implement the U2H map numerically and test its predictions against  WAVEWATCH III numerical simulations for both idealised and realistic current configurations. Our framework can be straightforwardly extended to relate characteristics of the wave field other than SWH such as Stokes drift to the currents.