{'fraction_non_alphanumeric': 0.03380281690140845, 'fraction_numerical': 0.0, 'mean_word_length': 4.427480916030534, '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}}
A stochastic model of sea-surface roughness. I. Wave crests

In this paper we develop a two-scale model of sea-surface roughness, in which for the first time the randomness of both long and short waves is taken fully into account. The model includes long–wave-short-wave interactions, dissipation of the short-wave energy by breaking, and regeneration by the wind. This leads to an integral equation for the short-wave steepness, which is solved by iteration. The effects of wind speed and of long-wave steepness upon the distribution of roughness at the long-wave crests are calculated and discussed. Also the effect of a band-width parameter for the long-wave spectrum. A random noise source can be included.