Nonlinear growth of swell by wind under cross sea

The development of swell under a cross sea was investigated because four drifting wave buoys in the marginal ice zone near the Chukchi Sea measured a wave event contrary to the waves expected following the fetch law. The expected sea state at the ice edge under southeasterly winds of 10–15 ms−1 was 2–3 m waves with a 6–7 s period from the southeast. However, the dominant buoy-measured wave was almost 90 degrees off the wind from the southwest with 2 m wave height and 9 s period. Since the phase speed was 14 ms−1 and the oblique wind speed was 10–15 ms–1, the wave age of the measured waves was >> 1. A hindcast model using the discrete interaction approximation (DIA) method, surprisingly, reproduced the buoy-measured swell including the direction. An analysis of the source terms revealed that the swell evolved over hundreds of kilometers across the ice-free ocean, and central to the swell development was the nonlinear coupling of wind energy input and the swell spectral peak via the nonlinear interactions source term. The implications of using the DIA were evaluated through idealized cross-sea simulations using the EXACT-NL model. The EXACT-NL simulations were qualitatively consistent with the DIA results and corroborated the hindcast finding. Moreover, the EXACT-NL simulations provided additional insights into the mechanisms of nonlinear energy transfer, which were found to align with the Masson (1993) theory of nonlinear coupling between swell and wind waves.