A New Theory of the Saturated Gravity Wave Spectrum for the Middle Atmosphere

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  • 1 Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland
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Abstract

A new theory of the saturated vertical wavenumber spectrum of gravity waves for the middle atmosphere is developed. The theory is based on a hypothesis that the saturated spectrum is a result of balance among various spectral sources and sinks of gravity waves in the middle atmosphere. The spectral source included in this paper is the amplification of upward propagating gravity waves due to the density effect. Two spectral sinks are the off-resonant wave-wave interactions and scale-dependent radiative damping. It is found that the algebraic approximation of the saturated vertical wavenumber spectrum of horizontal winds, F(μ), can be written as
Fμμ−3θμ2−1
,where μ is the dimensionless vertical wavenumber, and θ is a parameter measuring the ratio of the dynamic effect to the radiative effect on the dissipation. The theory predicts the widely cited −3 power law for both small and large vertical wavenumbers. However, when θ < 0.1 a significant range of wavenumbers exists for which F(μ) ∼ μp with 1 < p < 3. The model spectrum produced by F(μ) leads to a much better fit to a set of observed spectra than does the −3 power law. In addition, the effects of other spectral sources and sinks by photochemical processes and molecular diffusion in the middle atmosphere are discussed.

Abstract

A new theory of the saturated vertical wavenumber spectrum of gravity waves for the middle atmosphere is developed. The theory is based on a hypothesis that the saturated spectrum is a result of balance among various spectral sources and sinks of gravity waves in the middle atmosphere. The spectral source included in this paper is the amplification of upward propagating gravity waves due to the density effect. Two spectral sinks are the off-resonant wave-wave interactions and scale-dependent radiative damping. It is found that the algebraic approximation of the saturated vertical wavenumber spectrum of horizontal winds, F(μ), can be written as
Fμμ−3θμ2−1
,where μ is the dimensionless vertical wavenumber, and θ is a parameter measuring the ratio of the dynamic effect to the radiative effect on the dissipation. The theory predicts the widely cited −3 power law for both small and large vertical wavenumbers. However, when θ < 0.1 a significant range of wavenumbers exists for which F(μ) ∼ μp with 1 < p < 3. The model spectrum produced by F(μ) leads to a much better fit to a set of observed spectra than does the −3 power law. In addition, the effects of other spectral sources and sinks by photochemical processes and molecular diffusion in the middle atmosphere are discussed.
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