{'fraction_non_alphanumeric': 0.016933207902163686, 'fraction_numerical': 0.0, 'mean_word_length': 4.944134078212291, '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}}
Generation of transverse waves in a liquid layer with insoluble surfactant subjected to temperature gradient

The formation of Faraday waves (FWs) at the surfactant-covered free surface of a vertically vibrated liquid layer is considered. The layer is subjected to a vertical temperature gradient. The surfactant is insoluble. Linear stability analysis and the Floquet method are used for disturbances with arbitrary wave numbers to find the regions of critical vibration amplitude where FWs are generated. The problem is considered for the semi-infinite liquid layer, as well as for the layer of a finite depth. It is shown numerically, that in the semi-infinite case the critical tongue of a neutral stability curve corresponding to the lowest value of the forcing amplitude is related to the subharmonic instability mode. It changes to the harmonic one in the case of finite depth. The influence of thermocapillary Marangoni number on the critical amplitude of FWs is studied. The growth of that number stabilizes the system, however, this effect is very weak.