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Internal Solitary Waves in an Atmosphere with Thermal Inversion

M. C. ShenThe University of Wisconsin, Madison

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Abstract

This paper reports a study of solitary waves in a compressible atmosphere with a layer of cold air underneath a layer of warmer air of infinite height. The temperature of each layer is uniform. Two critical speeds and the first-order solitary wave solutions for both layers are obtained in terms of the temperature and mass flux ratios. The internal solitary wave may be a wave of elevation or depression, or may not appear at all. The amplitude of a wave of elevation (depression) increases (decreases) with the height and reaches a maximum (minimum) at the inversion interface, then stays at the maximum (minimum) value in the upper layer. The wave speed is found greater than the corresponding critical speed, and no solitary wave appears when the temperature of the atmosphere becomes uniform.

Abstract

This paper reports a study of solitary waves in a compressible atmosphere with a layer of cold air underneath a layer of warmer air of infinite height. The temperature of each layer is uniform. Two critical speeds and the first-order solitary wave solutions for both layers are obtained in terms of the temperature and mass flux ratios. The internal solitary wave may be a wave of elevation or depression, or may not appear at all. The amplitude of a wave of elevation (depression) increases (decreases) with the height and reaches a maximum (minimum) at the inversion interface, then stays at the maximum (minimum) value in the upper layer. The wave speed is found greater than the corresponding critical speed, and no solitary wave appears when the temperature of the atmosphere becomes uniform.

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