Modulation of Wind-Wave Breaking by Long Surface Waves

Abstract

This paper reports the results of field measurements of wave breaking modulations by dominant surface waves, taken from the Black Sea research platform at wind speeds ranging from 10 to 20 m/s. Wave breaking events were detected by video recordings of the sea surface synchronized and collocated with the wave gauge measurements. As observed, the main contribution to the fraction of the sea surface covered by whitecaps comes from the breaking of short gravity waves, with phase velocities exceeding 1.25 m/s. Averaging of the wave breaking over the same phases of the dominant long surface waves (LWs, with wavelengths in the range from 32 to 69 m) revealed strong modulation of whitecaps. Wave breaking occurs mainly on the crests of LWs and disappears in their troughs. Data analysis in terms of the modulation transfer function (MTF) shows that the magnitude of the MTF is about 20, it is weakly wind-dependent, and the maximum of whitecapping is windward-shifted from the LW-crest by 15 deg. A simple model of whitecaps modulations by the long waves is suggested. This model is in quantitative agreement with the measurements and correctly reproduces the modulations’ magnitude, phase, and non-sinusoidal shape.

On the Groupiness and Intermittency of Oceanic Whitecaps

“…This supports the amplitude analysis presented in Section 5.2, which showed enhanced breaking activity linked to the passage of energetic wave groups. Dominant wave crests have also been shown to be the preferential breaking regions for waves of various scales in previous field studies (Donelan et al, 1972;Dulov et al, 2002Dulov et al, , 2021Holthuijsen & Herbers, 1986;Yurovsky et al, 2017). A marked contrast exists, however, between the magnitude of long wave modulation of wave breaking in our results, which show a 2-5 fold enhancement of breaking probability attributed to wave groups, compared to those of Dulov et al (2002Dulov et al ( , 2021 who found modulation factors as high as 20-24.…”

“…Dominant wave crests have also been shown to be the preferential breaking regions for waves of various scales in previous field studies (Donelan et al, 1972;Dulov et al, 2002Dulov et al, , 2021Holthuijsen & Herbers, 1986;Yurovsky et al, 2017). A marked contrast exists, however, between the magnitude of long wave modulation of wave breaking in our results, which show a 2-5 fold enhancement of breaking probability attributed to wave groups, compared to those of Dulov et al (2002Dulov et al ( , 2021 who found modulation factors as high as 20-24. It is, however, important to keep in mind that our analysis sorts long waves into two categories, namely wave groups and the "background" wave field.…”

“…Conversely, the long-wave modulations of the breaking characteristics of the short waves have also been shown to impact the growth rate of the long waves due to changes in the form drag over the wave field induced by air flow separation in the breaking regions (Donelan et al, 2010;Kudryavtsev & Chapron, 2016). Dulov et al (2002Dulov et al ( , 2021 investigated the impact of long-wave modulations on the breaking characteristics of short waves using a combination of optical video imagery for breaker detection and an array of wave staffs for measuring the instantaneous sea-surface elevation within the camera footprint. They found strong modulation of the phase and amplitude of the instantaneous whitecap coverage, W, by dominant waves, with short-wave breaking most likely to occur at the crests of the long waves.…”

“…Inspired by the approaches of Dulov et al (2002), Yurovsky et al (2017), andDulov et al (2021), the current study investigates the modulation of wave breaking by dominant wave groups in terms of the time variability of the whitecap coverage W. We employ coherent (i.e., simultaneous and co-located) observations of W and the sea surface elevation, acquired with an optical stereo video camera system installed on a platform in the North Sea, to study the coincidence of elevated wave breaking activity and wave group passage. We also analyze the temporal intermittency and clustering tendencies of the whitecap coverage with the telegraph approximation (TA), a methodology that isolates the time variability of a time series from its amplitude variations.…”

Field Observations of Breaking of Dominant Surface Waves

“…where h(x * ) is the Heaviside function with x * = c p /(1 − δ) − c T , chosen so Q p vanishes when c of the entire spectral peak region are below c T set to 2 m s −1 , constant b 1 corresponds to our experimental data (6), constant b 2 = 1.39 × 10 −5 is chosen to match the data reported in [35] (see their Figure 4). The exponent n is set to 5 to be consistent with [62] and with the experimental findings of [35,63]. An example of model simulations of Q using ( 16) as a function of the wind speed for various α and p is shown in Figure 11.…”