Imprint of ocean currents on signicant wave height

Ocean currents have been observed to impact the spatial distribution of significant wave height (hereafter "Hs") of surface gravity waves profoundly, with implications for air-sea fluxes, extreme waves, and error budget in satellite observations. In this work, we derive analytic formulas that relate Hs to current velocities under the weak-current approximation, cross-validate the results with WAVEWATCH III, and find implications potentially useful for observational and modelling studies. 

First, we show that when swell-like surface waves interact with a localized current, caustics, where rays cross in real space, do not lead to singularities in Hs if the wave energy spectra have a realistic directional spread in wavenumber space. This has implications for understanding the origin of freak waves, where caustics have been postulated as a possible source. Then, we consider another regime where weak turbulent flows are considered. Analytic formulas are found that deterministically link the patterns of Hs to currents. The formulas' statistical counterparts are applied to study how the spectral slopes, amplitudes and directionality of Hs are related to currents. Our results demonstrate that the variations of Hs are controlled by the rotational component of the currents, suggesting the potential of using information from surface wave to infer current properties in real observations, or vice versa.