Effects of Coexisting Surface Waves on Propagation of a Surface Wave Train

Abstract Spectral surface wave models predict the wave action evolution of multiple wave components. It is well understood that the group speed of the wave action of a particular wave component is modified if an Eulerian near-surface current exists. However, a typical ocean wave field also introduces a significant integrated Stokes drift, or Lagrangian mass transport, and its impact on the group speed of a particular wave component is not well known. In this study, the wave evolution equations are derived in the presence of two wave trains, and the impacts of one wave train on the phase and group speeds of the other wave train are investigated. The results are extended to estimate the impact of the entire wave spectrum on the propagation of a particular wave train. It is found that the group speed of the dominant waves can be significantly enhanced by the presence of other waves, by up to 0.3–0.4 m s −1 or 4%–5%, in strongly wind-forced conditions under tropical cyclones. This increase of the group speed is almost twice as large as the advection by a sheared current with the same profile as the Stokes drift integrated over the wave spectrum. Introducing this enhanced group speed in the wave models may make a noticeable impact on their surface wave predictions. It is also found that the increase of the phase speed of a particular wave component is much larger than the advection by a sheared current with the same profile as the integrated Stokes drift.