{'fraction_non_alphanumeric': 0.019169329073482427, 'fraction_numerical': 0.006922257720979766, 'mean_word_length': 4.890282131661442, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Laboratory study of fine structure of the short surface waves due to breaking: two-directional wave propagation

This study was stimulated by the need to identify the influence of breaking on the evolution on the short surface wave field, responsible for microwave scattering. Laboratory measurements of the fine space-time structure of short gravity-capillary waves and Ku-band scattering at grazing and moderate incidence by spilling and plunging breaking waves in a laboratory wave channel are presented. Unsteady breaking waves are generated by focusing wave groups in space-time domains. A line-scanning laser slope gauge was used for measuring capillary-gravity waves from 2 mm to 20 cm wavelengths and frequency ranges up to 150 Hz. A dual polarized (VV, HH) coherent pulsed Ku-band scatterometer with temporal resolution of 3 ns was used to obtain simultaneously Doppler spectra of the scattered signals from the breaking area for grazing angles from 6 to 25 degrees. Two-dimensional filtering in the wave number-frequency plane, as well as plus/minus Doppler spectra was used to separate the direction of propagation of the surface waves within the breaking region. It was found that the breaking splash is the main source of the surface wave generation. The short surface wave slope fields field produced by breaking could be separated into short (4-8 mm wavelength) fast waves, having a phase velocity equal to the velocity of the crest of the breaking dominant 1 Hz waves, and free gravity-capillary waves. Both types of waves were found to co-and counter-propagate relative to the dominant wave propagation direction. The Doppler spectrograms reveal the presence of high frequency waves at the moment of breaking that can be associated with short fast waves. The low frequency part of the Doppler spectrogram is consistent with the appearance of free gravity waves.