A new breaker index introducing a two-phase nearshore dissipation condition

The breaker index ( γ ), which defines the breaker height-to-depth ratio, is recognized as a critical parameter for energy dissipation in nearshore wave models. Existing formulae often struggle with the complex, non-monotonic dependence of γ on hydrodynamic and bathymetric conditions. In this study, a new physics-based formula for γ , is introduced. The formula is derived from various extensive laboratory and field datasets. The analysis reveals a two-phase breaking behavior governed by a dynamic relative depth threshold, as a function of offshore wave steepness ( s o ). For relative depths below this threshold, γ variation exhibits an inverse trend compared to γ values for relative depths higher than this threshold, as a function of s o . Conventional models have not captured these dominant trends. The newly proposed formula, constructed as a piecewise linear function, explicitly models this conditional behavior. The formula's capability is confirmed against two independent field and laboratory validation datasets. The statistical assessment indicates a significant improvement of the breaker wave estimation in the surf-zone, applying the new formula. This result suggests that the accurate prediction of γ requires a conditional formulation accounting for the complex influences of relative depth and offshore steepness. • A new physics-based formula was developed for the breaker index ( γ ). • Non-monotonic, dual-regime dependency of γ on relative depth ( k p d ) was confirmed. • A dynamic breaking threshold ( k p d Thr ) with linear dependence on offshore steepness ( s o ) was shown. • An inverse behavior of γ depending on k p d values relative to a dynamic threshold. • Performance of the new formula outperformed previously established formulae.