A simplified wave enhancement criterion for moving extreme events

Abstract

An analytical model is derived to efficiently describe the wave energy distribution along the main transects of a moving extreme weather event. The model essentially builds on a generalization of the self-similar wave growth model and the assumption of a strongly dominant single spectral mode in a given quadrant of the storm. The criterion to anticipate wave enhancement with the generation of trapped abnormal waves defined as gr/ur2≈cT(ur/V)1/q, with r, u, and V, radial distance, average sustained wind speed, and translation velocity, respectively. Constants q and cT follow the fetch-law definitions. If forced during a sufficient time scale interval, also defined from this generalized self-similar wave growth model, waves can be trapped and large amplification of the wave energy will occur in the front-right storm quadrant. Remarkably, the group velocity and corresponding wavelength of outrunning wave systems will become wind speed independent and solely related to the translating velocity. The resulting significant wave height also only weakly depends on wind speed, and more strongly on the translation velocity. Compared to altimeter satellite measurements, the proposed analytical solutions for the wave energy distribution demonstrate convincing agreement. As analytically developed, the wave enhancement criterion can provide a rapid evaluation to document the general characteristics of each storm, especially the expected wavefield asymmetry.