A Simple Nearly Analytic Model of a Gravity Wave Driven Middle Atmosphere Circulation

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  • 1 Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon
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Abstract

A nearly analytic model of a gravity wave driven middle atmosphere circulation is formulated. The simplified model represents the one-dimensional interaction of a single gravity wave mode with a zonal-mean flow. Solutions of this model are shown to agree very well with numerical results from a more complete mean flow-gravity wave model (essentially the model developed by Holton). A single nondimensional parameter, the ratio of a mean flow radiative forcing parameter, and the gravity wave momentum flux incident into the middle atmosphere from below largely determines the solution of the model. For typical middle atmosphere parameter values, an approximate analytic solution can be obtained, and this solution permits the parameter dependence of the circulation to be characterized very simply. The gravity wave driven circulation extends downward from the level (the breaking level, approximately) where the momentum flux equals the mean flow radiative forcing. Stronger forcing implies higher breaking levels and stronger flows, while stronger flux (incident from below) yields lower breaking levels and weaker flows. Given the exponential growth of the flux in height, the breaking and jet maximum levels are relatively insensitive to the mean flow and gravity wave parameters; the zonal flow is “closed off” within the middle atmospheric region over a wide range of parameter values.

The nearly analytic model is briefly considered in relation to observations and modeling of Earth's middle atmosphere, and some of its limitations are discussed. It is also applied to the middle atmosphere of Mars.

Abstract

A nearly analytic model of a gravity wave driven middle atmosphere circulation is formulated. The simplified model represents the one-dimensional interaction of a single gravity wave mode with a zonal-mean flow. Solutions of this model are shown to agree very well with numerical results from a more complete mean flow-gravity wave model (essentially the model developed by Holton). A single nondimensional parameter, the ratio of a mean flow radiative forcing parameter, and the gravity wave momentum flux incident into the middle atmosphere from below largely determines the solution of the model. For typical middle atmosphere parameter values, an approximate analytic solution can be obtained, and this solution permits the parameter dependence of the circulation to be characterized very simply. The gravity wave driven circulation extends downward from the level (the breaking level, approximately) where the momentum flux equals the mean flow radiative forcing. Stronger forcing implies higher breaking levels and stronger flows, while stronger flux (incident from below) yields lower breaking levels and weaker flows. Given the exponential growth of the flux in height, the breaking and jet maximum levels are relatively insensitive to the mean flow and gravity wave parameters; the zonal flow is “closed off” within the middle atmospheric region over a wide range of parameter values.

The nearly analytic model is briefly considered in relation to observations and modeling of Earth's middle atmosphere, and some of its limitations are discussed. It is also applied to the middle atmosphere of Mars.

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