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 of the Atmospheric Sciences – American Meteorological Society
Published: Aug 29, 2017
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