{'fraction_non_alphanumeric': 0.02181208053691275, 'fraction_numerical': 0.0, 'mean_word_length': 5.489130434782608, '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}}
TRAPPED MODES AROUND FREELY FLOATING BODIES IN TWO-LAYER FLUIDS

We consider the coupled system modeling the interaction of time-harmonic progressive water-waves with an array of three-dimensional freely floating obstacles in a two-layer fluid. Presenting a variational and operator formulation for the problem and a condition guaranteeing the existence of trapped waves, we give a number of examples of floating structures supporting trapped waves. We also study how the problem parameters (density ratio, obstacle dimensions, layer depths and radian frequency) influence the trapping condition.