Nonlinear Behavior in the Propagation of Atmospheric Gravity Waves

Patricia M. Franke Department of Electrical and Computer Engineering, University of Illinois, Urbana–Champaign, Urbana, Illinois

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Walter A. Robinson Department of Atmospheric Sciences, University of Illinois, Urbana–Champaign, Urbana, Illinois

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Abstract

The nonlinear behavior of quasi-monochromatic gravity wave breaking events is studied using a high-resolution, two-dimensional, fully nonlinear numerical model. A suite of supporting models is used alongside the nonlinear model to separate the effects of wave–wave and wave–mean flow interactions. The focus of this study is the breaking of initially monochromatic waves at two different frequencies. The results are used to address some of the issues central to the role that nonlinear effects play in gravity wave propagation and saturation.

It is found that the presence or absence of wave–mean flow interactions influences the nature of wave breaking. Comparison of the results from the fully nonlinear model with those from a model from which the wave–mean flow interactions are removed indicates that wave overturning and breaking occur at lower altitudes when wave–mean flow interactions are included. This influence is found to be frequency dependent with the effect being stronger at the higher frequencies. Breaking is also less vigorous in the lower-frequency case because some of the higher harmonics generated by wave–wave interactions can propagate as gravity waves, implying that regions of breaking can be a source of new gravity waves. Spectral analyses of the results show that a rapid and dramatic spread in wavenumber and frequency occurs only when the full complement of nonlinearities is present. The implications of these results for observational and theoretical studies are discussed.

Corresponding author address: Patricia Franke, 3380 Mitchell Lane, Boulder, CO 80301.

Email: pfranke@colorado-research.com

Abstract

The nonlinear behavior of quasi-monochromatic gravity wave breaking events is studied using a high-resolution, two-dimensional, fully nonlinear numerical model. A suite of supporting models is used alongside the nonlinear model to separate the effects of wave–wave and wave–mean flow interactions. The focus of this study is the breaking of initially monochromatic waves at two different frequencies. The results are used to address some of the issues central to the role that nonlinear effects play in gravity wave propagation and saturation.

It is found that the presence or absence of wave–mean flow interactions influences the nature of wave breaking. Comparison of the results from the fully nonlinear model with those from a model from which the wave–mean flow interactions are removed indicates that wave overturning and breaking occur at lower altitudes when wave–mean flow interactions are included. This influence is found to be frequency dependent with the effect being stronger at the higher frequencies. Breaking is also less vigorous in the lower-frequency case because some of the higher harmonics generated by wave–wave interactions can propagate as gravity waves, implying that regions of breaking can be a source of new gravity waves. Spectral analyses of the results show that a rapid and dramatic spread in wavenumber and frequency occurs only when the full complement of nonlinearities is present. The implications of these results for observational and theoretical studies are discussed.

Corresponding author address: Patricia Franke, 3380 Mitchell Lane, Boulder, CO 80301.

Email: pfranke@colorado-research.com

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