Spectral analysis of the free surface fluctuations behind microbreakers

Small-scale surface fluctuations taking place behind steady breaking waves has received attention in quite distinct research frameworks, from naval hydrodynamics to geophysical applications, with many papers primarily concerned with the remote sensing, radar or infrared, of the ocean surface (see [1] and [11], for instance). Short wavelength spilling breakers, also referred as 'micro-breakers' are usually originated by the wind and play an important role in terms of momentum, heat and gas exchange between atmosphere and ocean. At this short scales, due to the strong action of surface tension, the characteristic plunging jet is replaced by a bulge which slides down along the forward face of the wave [12]. Since the breaking takes place without wave overturning, the amount of air entrained is significantly reduced [8]. The generation and the downstream propagation of free surface ripples have been subject of intense research studies. In [6], by using the dispersive focusing technique, very gentle breakers have been generated experimentally by progressively reducing the amplitude of the wavemaker motion. It has been shown that, at the early stage of the breaking establishment, the bulge grows while the toe is substantially fixed with respect to the crest. In a next stage, the bulge begins to slide down upon the forward face of the wave and a shear layer develops between the gravity induced downslope flow near the free surface and the underlying upslope flow. Instabilities of this shear layer eventually lead to the formation of a train of downstream propagating ripples. In [7] and [5] a submerged hydrofoil has been used to produce a quasi-steady breaking and the frequency and wavenumber spectra of the downstream propagating surface fluctuations have been analysed. Comparisons with a theoretical model confirmed that shear flow instabilities are the primary mechanism for ripples generation. An accurate analysis of the space-time behaviour of the surface fluctuations behind steady breakers has been carried out also in [13]. Wavenumber-frequency spectra show that ripples' wavelength grows during their downstream motion while the temporal frequency of fluctuations, recorded at different longitudinal position, remains substantially constant. This led authors to speculate that ripples behaves like surface waves on a spatially varying current.