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The Response of the Lower Stratosphere to Zonally Symmetric Thermal and Mechanical Forcing

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  • 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom
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Abstract

The response of the atmosphere to zonally symmetric applied heating and mechanical forcing is considered, allowing for the fact that the response may include a change in the wave force (or “wave drag”). A scaling argument shows that an applied zonally symmetric heating is effective in driving a steady meridional circulation provided that the wave force (required to satisfy angular momentum constraints) is sufficiently sensitive to changes in the mean flow in the sense that the ratio is large, where K is a measure of the sensitivity of the wave force; α, N, and f are the radiative damping rate, buoyancy frequency, and Coriolis parameter, respectively; and and are the horizontal and vertical length scales of the heating, respectively. Furthermore, in the “narrow heating” regime where this ratio is large, the structure of the meridional circulation response is only weakly dependent on the details of the wave force. The scaling arguments are verified by experiments in a dry dynamical circulation model. Consistent with the scaling prediction, the regime does not apply when the width of the imposed heating is increased. The narrow-heating regime is demonstrated to be relevant to the double peak in tropical lower-stratospheric upwelling considered in a companion paper, supporting the hypothesis that this feature is radiatively driven. Similar arguments are applied to show that a narrow zonally symmetric applied mechanical forcing is primarily balanced by a change in wave force. This provides an explanation for the recently identified compensation between resolved and parameterized waves in driving modeled trends in the Brewer–Dobson circulation.

Corresponding author address: Alison Ming, DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom. E-mail: a.ming@damtp.cam.ac.uk

Abstract

The response of the atmosphere to zonally symmetric applied heating and mechanical forcing is considered, allowing for the fact that the response may include a change in the wave force (or “wave drag”). A scaling argument shows that an applied zonally symmetric heating is effective in driving a steady meridional circulation provided that the wave force (required to satisfy angular momentum constraints) is sufficiently sensitive to changes in the mean flow in the sense that the ratio is large, where K is a measure of the sensitivity of the wave force; α, N, and f are the radiative damping rate, buoyancy frequency, and Coriolis parameter, respectively; and and are the horizontal and vertical length scales of the heating, respectively. Furthermore, in the “narrow heating” regime where this ratio is large, the structure of the meridional circulation response is only weakly dependent on the details of the wave force. The scaling arguments are verified by experiments in a dry dynamical circulation model. Consistent with the scaling prediction, the regime does not apply when the width of the imposed heating is increased. The narrow-heating regime is demonstrated to be relevant to the double peak in tropical lower-stratospheric upwelling considered in a companion paper, supporting the hypothesis that this feature is radiatively driven. Similar arguments are applied to show that a narrow zonally symmetric applied mechanical forcing is primarily balanced by a change in wave force. This provides an explanation for the recently identified compensation between resolved and parameterized waves in driving modeled trends in the Brewer–Dobson circulation.

Corresponding author address: Alison Ming, DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom. E-mail: a.ming@damtp.cam.ac.uk
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