Beyond the rigid lid: Baroclinic modes in a structured atmosphere

Beyond the rigid lid: Baroclinic modes in a structured atmosphere AbstractThe baroclinic-mode decomposition is a fixture of the tropical-dynamics literature due to its simplicity and apparent usefulness in understanding a wide range of atmospheric phenomena. However, its derivation relies on the assumption that the tropopause is a rigid lid, which artificially restricts the vertical propagation of wave energy. This causes tropospheric buoyancy anomalies of a single vertical mode to remain coherent for all time in the absence of dissipation. Here, we derive the Green’s functions for these baroclinic modes in a two-dimensional troposphere (or, equivalently, a three-dimensional troposphere with one translational symmetry) that is overlain by a stratosphere. These Green’s functions quantify the propagation and spreading of gravity waves generated by a horizontally localized heating, and they can be used to reconstruct the evolution of any tropospheric heating. For a first-baroclinic two-dimensional right-moving or left-moving gravity wave with a characteristic width of 100 km, its initial horizontal shape becomes unrecognizable after 4 hours, at which point its initial amplitude has also been reduced by a factor of 1/π. After this time, the gravity wave assumes a universal shape that widens linearly in time. For gravity waves on a periodic domain the length of Earth’s circumference, it takes only 10 days for the gravity waves to spread their buoyancy throughout the entire domain. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Atmospheric Sciences American Meteorological Society

Beyond the rigid lid: Baroclinic modes in a structured atmosphere

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Publisher
American Meteorological Society
Copyright
Copyright © American Meteorological Society
ISSN
1520-0469
D.O.I.
10.1175/JAS-D-17-0140.1
Publisher site
See Article on Publisher Site

Abstract

AbstractThe baroclinic-mode decomposition is a fixture of the tropical-dynamics literature due to its simplicity and apparent usefulness in understanding a wide range of atmospheric phenomena. However, its derivation relies on the assumption that the tropopause is a rigid lid, which artificially restricts the vertical propagation of wave energy. This causes tropospheric buoyancy anomalies of a single vertical mode to remain coherent for all time in the absence of dissipation. Here, we derive the Green’s functions for these baroclinic modes in a two-dimensional troposphere (or, equivalently, a three-dimensional troposphere with one translational symmetry) that is overlain by a stratosphere. These Green’s functions quantify the propagation and spreading of gravity waves generated by a horizontally localized heating, and they can be used to reconstruct the evolution of any tropospheric heating. For a first-baroclinic two-dimensional right-moving or left-moving gravity wave with a characteristic width of 100 km, its initial horizontal shape becomes unrecognizable after 4 hours, at which point its initial amplitude has also been reduced by a factor of 1/π. After this time, the gravity wave assumes a universal shape that widens linearly in time. For gravity waves on a periodic domain the length of Earth’s circumference, it takes only 10 days for the gravity waves to spread their buoyancy throughout the entire domain.

Journal

Journal of the Atmospheric SciencesAmerican Meteorological Society

Published: Aug 29, 2017

References

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