Contardo, S.; Lowe, R.; Hansen, J. E., and Dufois, F., 2024. Quantification of nearshore long wave energy. In: Phillips, M.R.; Al-Naemi, S., and Duarte, C.M. (eds.), Coastlines under Global Change: Proceedings from the International Coastal Symposium (ICS) 2024 (Doha, Qatar). Journal of Coastal Research, Special Issue No. 113, pp. 584-588. Charlotte (North Carolina), ISSN 0749-0208.

As non-breaking short-wave groups propagate toward the shoreline, they are accompanied by bound long waves. Simultaneously, in response to depth gradients, free long waves are generated which propagate faster than the group. The amplitudes of bound and free long waves, and their phase relationships depend on the frequencies of the short and long waves and on the depth and bed slope. These long waves often play a major (or even dominant) role on water level variability in the nearshore, yet approaches to estimate how different long wave motions are generated by different mechanisms are incomplete. Here we aim to quantify the long-wave amplitude and phase relationship as the short-wave groups propagate over a slope, using a discrete linear analytical model. We find that the total long wave amplitude relative to the bound long wave amplitude is larger for milder bed slopes and with wind-sea conditions than for steeper bed slopes and with swell conditions. The results collapse as a function of the normalised bed slope (bed slope relative to long-wave frequency), for fixed values of the short-wave period. The role of the phase relationships between free and bound long waves is critical in determining the total long wave amplitude, with depth, bed slope and frequency being very important in determining this phase relationship.