On self-similarity of waves in tropical cyclones

Wave fields generated by tropical cyclones (TC) are of strong interest for marine engineering, navigation safety, determination of coastal sea levels and coastal erosion. Considerable efforts have been made to improve knowledge about the surface waves in TC, both from measurements and numerical experiments. Full sophisticated spectral wave models certainly have the capability to provide detailed wave information, but they require large computer power, precise well-resolved surface winds and/or needs to consider large ensembles of solutions. In this context, more simplified but robust solutions are demanded.

This work is based on 2D-parametric model of waves evolution forced by wind field varying in space and time, non-linear wave interactions and wave breaking dissipation [submitted to J. Geoph. Res., see also preprint DOI: https://doi.org/10.1002/essoar.10504620.1]. Numerical solutions of model provide efficient visualization on how waves develop under TC and leave it as swell. Superposition of wave-rays exhibits coherent spatial patterns of wave parameters depending on TC characteristics, - maximal wind speed (um), radius (Rm), and translation velocity (V).

In this presentation we demonstrate how solutions of 2D-parametric model can be described analytically through self-similar functionsusing proper scaling involving the main TC parameters: um, Rm, and V. These self-similar solutions can be treated as TC-wave Geophysical Model Function (TC-wave GMF), to help analytically derive azimuthal-radial distributions of the primary wave system parameters (SWH, wavelength, direction) under TC characterized by arbitrary sets of um, Rm and V conditions. Self-similar solutions describe the main properties of wave field under TC, in particular: right-to-left half asymmetry of wave field under TC; strong dependence of wave energy and wavelength on V, um and Rm caused by group velocity resonance; division of TCs on “slow” and “fast” when TC-induced waves outrun TC and form wake of swell trailing TC.

Comparisons between self-similar solutions and measurements of TC-generated waves reported in the literature, demonstrate excellent agreement to warrant their use for research and practical applications.

The core support for this work was provided by the Russian Science Foundation through the Project №21-47-00038 at RSHU. The support of the Ministry of Science and Education of the Russian Federation under State Assignment No. 0555-2021-0004 at MHI RAS, and State Assignment No. 0736-2020-0005 at RSHU are gratefully acknowledged.