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Abstract

From the equations of classical tidal theory with Newtonian cooling (Chapman and Lindzen, Atmospheric Tides: thermal and gravitational, Reidel, 1970), formulae are obtained for wind, temperature and pressure oscillations generated by thermal, gravitational and lower-boundary excitations of given frequency. The analysis is an extension of that of Butler and Small (Proc. R. Soc. Lond. A274, 91, 1963) who formulated solutions of the vertical structure equation in terms of two independent solutions of the homogeneous equation and derived expressions for surface pressure oscillations. A comprehensive formulation is presented for wind, temperature and pressure oscillations as functions of height with the above-mentioned sources of excitation and an upper-boundary radiation condition. The formulae obtained are applied at the surface leading to evaluations of the surface oscillation weighting function Wp(z) which weights the thermal excitation at height z according to its differential contribution to the surface oscillation. The formulae are shown to simplify at heights above a region of excitation and evaluations are undertaken of the thermal response weighting function Wt(z) which weights the thermal excitation at height z according to its differential contribution to the oscillation at any height above the region of thermal excitation. Computational procedures are described for obtaining two independent solutions of the homogeneous equation and results are presented for an adopted profile of atmospheric scale height. The problem of deriving the surface pressure oscillation due to a tidal potential is briefly reviewed and results are presented as an example of the application of formulae that have been derived.