On the Modulation of Shorter Windwaves by Longer Waves under Extreme Wind Forcing

The ocean surface is usually a mixture of shorter windwaves and longer swells, which in turn modulate the growth of the shorter windwaves under wind forcing. For example, the Southern Ocean is one of the world's most dynamic ocean zones with high wind forcing and extreme-fetch swells. Coupling with swell propagation and wind forcing is vital to the accurate predictions of wave models in the circumstances where wind-waves under high wind forcing are being modulated by longer waves (Babanin et al. 2019). In coastal areas, the presence of longer tidal waves amplifies the short windwaves under storms, leading to an elevation of incident wave height called "the tidal push” (Ho et al. 2021). Therefore, how the long waves modulate short windwave growth under high wind forcing is of great importance in the field of air-sea interaction. Unfortunately, the paucity of comprehensive data, exacerbated by measurement challenges, has led to a reliance on elusive interpretations and highly empirical parameterizations within numerical wave models. Tan et al. (2023) addressed that the sheltering coefficient, a crucial key parameter commonly used in the wave models that has been treated as a constant for decades, is in fact correlated with wind forcing and wave steepness based on experimental research. However, the scope of their investigation lacked a systematic exploration of the impact of long waves on short waves, with considerations for diverse wind forcing magnitudes, different wave types (monochromatic/JONSWAP), and long wave amplitudes

Therefore, to fill this gap, we carried out research in the SUrge STructural AIr-Sea INteraction Facility (SUSTAIN) located in University of Miami. We used two initial paddle wave types (regular monochromatic and irregular JONSWAP spectrum waves) and a wind-only experiment for comparison (no paddle waves). We subjected these background conditions under a wide range of wind forcing from a mild sea breeze to a Category 4 hurricane. We found 3 regimes of wave development with increasing wind forcing: 1. The “warm-up” phase (U10 < 10 m/s, mild sea breeze): capillary gravity wave begins to form uniformly on the paddle waves’ surface. At this phase, no strong modulation from paddle waves were observed. 2. The “development” phase (10 m/s < U10 < 37 m/s, rough sea to tropical storm intensity): strong suppression of wind-waves by paddle waves was observed. At this phase, monochromatic paddle waves began to grow while the shorter wind-waves remained suppressed. In the meantime, the drag coefficient increased drastically, which signified a very high momentum transfer from winds to waves. 3. The “saturation” phase (U10 > 37 m/s, hurricane intensity): at this phase intense breaking of paddle waves took place. Both the drag coefficient and paddle wave energy were saturated with further increase of wind forcing. However, the shorter wind-wave energy began to grow. This is due to long paddle waves’ breaking, which “liberated” the suppression of shorter waves from long paddle waves and allowed them to grow. The suppression ratio of long monochromatic waves on shorter windwaves from our research agrees well with the model predicted by Chen and Belcher (2000). The sheltering coefficient from our results in the range with Tan et al. (2023). Furthermore, we showed that the sheltering coefficient decreases with increasing long wave amplitude and follows a “U” shape (first decrease then increase) with increasing wind forcing. Finally, we will incorporate our parameterization in Wavewatch III model, deepen the understanding of the long waves’ modulation on short waves, and eventually provide guidance on future field campaign observations and the development of next generation wave models.