The 2D‐parametric model suggested in the companion paper is used to simulate waves under Tropical Cyclones (TCs). Set of equations describing both wind waves and swell evolution in space and time, is solved using the method of characteristics. Wave‐ray patterns efficiently chart on how wave trains develop and travel through the TC varying wind field, to leave the storm area as swell systems.

Depending on TC main characteristics, ‐ maximal wind speed (um), radius (Rm), and translation velocity (V), wave‐train rays superpose to exhibit particular coherent spatial patterns of significant wave height, peak wavelength and direction. Group velocity resonance leads to the appearance of waves with abnormally high energy, further outrunning as long swell systems through the TC front sector. Yet, when the TC translation velocity exceeds a threshold value, waves cannot reach group velocity resonance, and travel backwards, to form a wake of swell systems trailing the forward moving TC.

Importantly, the model solutions for TC 2D‐wave fields can be parameterized using 2D self‐similar universal functions. Comparisons between self‐similar solutions and measurements, demonstrate a reasonable agreement to warrant scientific and practical applications. Self‐similar solutions provide immediate estimates of azimuthal‐radial distributions of wave parameters under TCs, solely characterized by arbitrary sets of um, Rm and V conditions. Self‐similar solutions clearly divide TCs between slow TCs, fulfilling conditions Rm/Lcr>1, and fast TCs corresponding to Rm/Lcr<1, where Lcr is a critical fetch. Around the region Rm/Lc= 1, group velocity resonance occurs, leading to the largest possible waves generated by a TC.

Plain Language Summary

A practical and rapid evaluation of wave conditions under Tropical Cyclone (TC) is often required for navigation safety and coastal hazards. Building on the fully consistent 2D‐parametric model suggested in the companion paper, a method is presented to map the distribution of wave energy, peak frequency and direction along wave‐rays. Wave‐rays help to visualize how wave trains develop and travel through the TC varying wind field, and how they leave the storm area as swell systems. Depending on the main TC characteristics, ‐ maximal wind speed (um), radius (Rm), and translation velocity (V)‐, the most striking feature of wave fields is generally a strong azimuthal asymmetry, resulting from group velocity resonance between traveling waves and moving TC. This effect can lead to extreme waves, further outrunning as swell forerunners in the TC heading direction. Importantly, it is demonstrated that immediate directional characteristics of TC wave fields can be evaluated using 2D self‐similar universal functions. For scientific and practical applications, these solutions provide fast estimates of waves generated by moving TC with arbitrary sets of um, Rm and V.