Nonlinear Growth of Swell by Wind under Cross Sea

Abstract 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 m s −1 was 2–3-m waves with a 6–7-s period from the southeast. However, the dominant buoy-measured wave was almost 90° off the wind from the southwest with a 2-m wave height and a 9-s period. Since the phase speed was 14 m s −1 and the oblique wind speed was 10–15 m s −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 interaction source term. The implications of using the DIA were evaluated through idealized cross-sea simulations using the exact nonlinear (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 theory of nonlinear coupling between swell and wind waves. Significance Statement Realistic formulations of physical processes occurring near the ocean surface are essential for the accuracy of ocean wave forecasts that we use for a wide range of recreational and engineering applications. To evaluate whether a model can reproduce complex sea conditions, validation against observations is important. We investigated a complex cross-sea condition using drifting wave buoy observations and wave model results and revealed a mechanism that allowed swell waves to grow over hundreds of kilometers when the wind was blowing from oblique directions. The cross sea is a well-known hazard for shipping, and our study presented a new insight into the swell evolution under a cross sea.