A Note on the second-order contribution to extreme waves generated during hurricanes - McAllister, M; Adcock, T; Taylor, P; Van Den Bremer, T (American Society of Mechanical Engineers, 2019)
High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behaviour. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (J. Geophys. Res. Oceans vol. 111, 2006). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are supported by experimental observations. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealised directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.