{'fraction_non_alphanumeric': 0.014644351464435146, 'fraction_numerical': 0.009414225941422594, 'mean_word_length': 4.835365853658536, '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}}
Sand ripples under sea waves Part 1. Ripple formation

In the present paper we formulate a predictive theory of the formation of sand ripples under sea waves. The theory is based on a linear stability analysis of a flat sandy bottom subject to a viscous oscillatory flow. The conditions for decay or amplification of a bottom perturbation are determined along with the wavelength of the most unstable component as a function of the Reynolds number of the flow and of the Froude and Reynolds numbers of the sediments. A comparison between theoretical findings and experimental data supports the validity of the present theory. An analytical solution for viscous oscillatory flow over a small-amplitude wavy bottom is determined for arbitrary values of the ratio r between the amplitude of fluid displacement and the wavelength of bottom waviness. Previous works by Lyne (1971) and Sleath (1976), who considered small or large values of r, are thus extended.