Nonlinear resonance in the wave–shoreline system: mechanisms and global expression

Abstract. Shoreline variability is commonly interpreted through linear links with external forcings, yet many coastal systems display oscillatory modes whose origin cannot be traced to any single forcing frequency. Here, we show that a robust and regionally recurrent quasi-biennial (20–30 month) mode of shoreline variability emerges from a nonlinear triadic resonance between the semi-annual (≈6 month) components of wave energy and the corresponding delayed shoreline response. Using satellite-derived shoreline time series (1993–2019), a set of known environmental drivers, and an iterative cross-EOF method to remove all linear forcing contributions, we identify a persistent residual peak centered at 24–26 months that is absent from the forcing spectra themselves. This peak arises from resonance between two near semi-annual frequencies, specifically through excitation of the shoreline by semi-annual wave forcing that produces a phase-shifted (lagged) near semi-annual shoreline response. The semi-annual wave forcing originates from two mechanisms: (1) phase opposition between local wind-sea and remote swell along eastern boundary systems, and (2) asymmetric annual wind forcing in monsoonal regions and semi-enclosed basins. A global triadic phase-coupling analysis confirms that these near semi-annual components interact nonlinearly to inject energy at the difference frequency, producing the emergent ≈24-month mode, which represents, on average, 15 % of the total dataset's shoreline variance in resonance-prone regions. These results establish nonlinear resonance as a fundamental and previously overlooked mechanism shaping shoreline variability at regional scales, with implications for understanding and predicting coastal response to changes in storm seasonality and wave-climate asymmetry.