Self-Similarity of Surface Wave Developments Under Tropical Cyclones

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 (u(m)), radius (R-m), 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-wavefields 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 u(m), R-m, and V conditions. Self-similar solutions clearly divide TCs between slow TCs, fulfilling conditions R-m/L-cr > 1, and fast TCs corresponding to R-m/L-cr < 1, where L-cr is a critical fetch. Around the region R-m/L-c = 1, group velocity resonance occurs, leading to the largest possible waves generated by a TC.