{'fraction_non_alphanumeric': 0.0109204368174727, 'fraction_numerical': 0.0, 'mean_word_length': 5.0, '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}}
On the application of the Boussinesq approximation for nonlinear gravity waves in the atmosphere

The name and the implications of the Boussinesq approximation for gravity waves in an incompressible, infinitely stratified atmosphere at rest are discussed together with the conditions for its validity. The most important conclusion is that for this approximation to be valid, the relative amplitude of the wave, with respect to the equilibrium value, has to be much smaller than the quotient of the wavelength in the direction of the density gradient and the length of that gradient. In its turn this product has to be much smaller than one.