The Lateral Transport of Zonal Momentum Due to Kelvin Waves in a Meridional Circulation

Abstract

A modified, equatorial Kelvin wave solution is obtained in the presence of the zonal-mean meridional circulation. The modified Kelvin wave solution, which is obtained via a perturbation expansion of the linearized, primitive equations on an equatorial ? plane, possesses a nonzero meridional wind component. This meridional wind component is absent when the background flow is at rest. The combination of the meridional and zonal winds induces a meridional flux of zonal momentum in the upstream direction of the background north?south flow. This flux is divergent in latitude and produces a nonzero wave-induced force even though the waves are linear, steady, and conservative. It is shown that, although such a force violates the traditional nonacceleration theorem in which the mean meridional circulation is negligible at leading order, the result is in accord with a more general nonacceleration theorem obtained from the exact generalized Lagrangian-mean theory in which the mean meridional circulation is nonzero. The meridional circulation, in effect, attempts to advect wave pseudomomentum off the equator, resulting in a nonzero acceleration in the Eulerian reference frame. The meridional flux of momentum for any equatorially trapped mode is derived from the generalized Lagrangian-mean theory. Those modes with eastward (westward) intrinsic phase velocity transport eastward (westward) zonal momentum in the upstream direction of the background meridional flow in the neighborhood of the equator. It is also shown that the vertical flux of zonal momentum is not constant with altitude in a steady vertical flow since diabatic heating/cooling is needed to sustain the vertical wind. Implications of the results for the terrestrial and Venusian atmospheres are discussed.