On the Dynamic Atmospheric Response to the Chandler Wobble Forcing

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  • 1 Center for Climatic Research, Institute for Environmental Studies, University of Wisconsin-Madison, 53706
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Abstract

A simple form of atmospheric tidal theory is used to deduce the dynamic atmospheric response to the nearly periodic 14 month precession of the Earth's rotation axis about its mean position, known as Chandler wobble. The departure of the tide from equilibrium, and the associated horizontal velocity field are calculated for an atmosphere initially at rest and having a constant adiabatic lapse rate with height. Results are in close agreement with those obtained from simple quasi-static approximations to the shallow water equations. The equilibrium tide in surface pressure is small, of order 10−3 mb, for typical polar displacements. The departure of the tide from equilibrium is still smaller, of order 10−6 mb, with associated horizontal velocities of order 10−6 m s−1. Inclusion of a reasonable solid body rotation component in the basic state does not qualitatively alter these results, although the non-equilibrium components are enhanced by nearly an order of magnitude, relative to those for a basic state at rest. The conclusion, qualified by numerous assumptions, is that the atmospheric response in surface pressure and horizontal velocity to the Chandler wobble forcing is of negligible amplitude.

Abstract

A simple form of atmospheric tidal theory is used to deduce the dynamic atmospheric response to the nearly periodic 14 month precession of the Earth's rotation axis about its mean position, known as Chandler wobble. The departure of the tide from equilibrium, and the associated horizontal velocity field are calculated for an atmosphere initially at rest and having a constant adiabatic lapse rate with height. Results are in close agreement with those obtained from simple quasi-static approximations to the shallow water equations. The equilibrium tide in surface pressure is small, of order 10−3 mb, for typical polar displacements. The departure of the tide from equilibrium is still smaller, of order 10−6 mb, with associated horizontal velocities of order 10−6 m s−1. Inclusion of a reasonable solid body rotation component in the basic state does not qualitatively alter these results, although the non-equilibrium components are enhanced by nearly an order of magnitude, relative to those for a basic state at rest. The conclusion, qualified by numerous assumptions, is that the atmospheric response in surface pressure and horizontal velocity to the Chandler wobble forcing is of negligible amplitude.

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