Abstract
2D-parametric model is used to simulate waves under Tropical Cyclones
(TCs). Set of equations describing either wind waves development and
swell evolution, is solved using method of characteristics. Wave-rays
patterns provide efficient visualization on how wave trains develop and
travel through TC varying wind field and leave storm area as swell.
The superposition of wave-trains rays exhibits coherent spatial patterns
of significant wave height, peak wavelength and direction, depending on
TC characteristics, - maximal wind speed (um), radius (Rm), and
translation velocity (V). Group velocity resonance leads to appearance
of waves with abnormal energy between the TC right and front sectors,
further outrunning as swell through the TC front sector. Yet, when TC
translation velocity exceeds a threshold value, waves cannot reach group
velocity resonance, and travelling backwards, form a wake of swell
systems trailing the forward moving TC.
2D-parametric model solutions are parameterized using 2D self-similar
universal functions. Comparisons between self-similar solutions and
measurements, demonstrate excellent agreement to warrant their use for
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. The region around
Rm/Lc = 1 corresponds to the group velocity resonance conditions,
leading to the largest possible waves generated by a TC.