A fully consistent 2D parametric model of wave development under spatially and/or time varying winds is developed. Derived coupled equations are written in their characteristic form to provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are developing and distributed under varying wind forcing conditions. For young waves, non‐linear interactions drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are governing the wave energy evolution. With a prescribed wind wave growth rate, proportional to (u*/c) squared, wave breaking dissipation must follow a power‐function of the dominant wave slope. For uniform wind conditions, this choice for the growth rate imposes solutions to follow fetch laws, with exponents q=‐1/4, p=3/4 correspondingly. This set of exponents recovers the Toba’s laws, and imposes the wave breaking exponent equal to 3. A varying wind direction can then drive spectral peak direction changes, leading to the occurrence of focusing/defocusing wave groups over localized areas where wave‐rays merge and cross. Significant (but finite) local variations of the energy are then expected under varying wind forcing. Propagating away from a stormy area, wave rays generally diverge, leading to dispersive swell systems.

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Plain Language Summary

A practical and rapid evaluation of wave conditions under stormy conditions is often required for navigation safety and coastal hazards. Surface waves and breakers are also essential components of the air‐ocean coupled system to possibly control the dynamical evolution of extreme events. Here, a fully consistent 2D parametric model for wave development is solved in the storm frame of reference. Along wave‐rays, peak energy and frequency evolve. Wave‐rays can also bend under changes of the wind direction. The proposed method thus helps rapidly identify localized areas where wave‐rays can merge or cross, leading to dangerous sea state hot spots. The suggested model will efficiently complement operational wave models, to simulate and map surface wave developments generated by moving Tropical and extra‐Tropical Cyclones.