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N. J. Lordi, A. Kasahara, and S. K. Kao

Abstract

A 26-level primitive equation spherical harmonic spectral model allowing for both wave-wave and wave-zonal flow interactions is developed for the study of stratospheric sudden warmings simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. The fist two cases, designated N1 and L1, involve both wave-wave and wave-zonal flow interactions and only wave-zonal flow interactions, respectively, with wavenumber 1 forcing. The other two cases, N2 and L2, are the same as N1 and L1, respectively, except for wavenumber 2 forcing.

Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere particularly in case N1 as manifested by the split in the initial polar vortex into a quasi-wavenumber 2 pattern. Also in case N1 the weighted geopotential amplitude of wavenumber 2 is as much as 70% that of wavenumber 1. There is a tendency toward an out-of-phase relationship between the weighted geopotential amplitudes of wavenumbers 1 and 2 in the course of time integration. In fact, just prior to the sudden warming, the weighted geopotential amplitude of wavenumber 2 reaches maximum, while that of wavenumber 1 starts to weaken.

In cases N1 and N2 at 60°N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. Eventually two separate easterly layers are merged. The linear cases L1 and L2 exhibit warmings which are both more shallow and more intense at 30 km than the nonlinear cases. Wave-wave interactions present in cases N1 and N2 seem to moderate the restoring forces on the zonal flow contributed by Rayleigh friction and Newtonian cooling/heating included in the model. Comparisons of the present results with those of Matsuno (1971), Holton (1976) and Schoeberl and Strobel (1980) are discussed.

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S-K. Kao, C. Y. Tsay, and Larry L. Wendell

Abstract

The wavenumber-frequency spectra of the meridional transport of angular momentum at 100, 200 and 500 mb, at 20, 40, 60 and 80N, show that there exist definite spectral domains of wave interactions between the zonal and meridional velocities at various latitudes. In the middle latitudes near 40N, the spectral band of the meridional transport of angular momentum is oriented from a region of low wavenumbers and low frequencies to a region of high wavenumbers and negative frequencies designated for eastward-moving waves. In low latitudes, however, the spectral band is confined to a narrow band centered near zero frequency.

An analysis of the linear and nonlinear contributions to the meridional transport of angular momentum in various wavenumber-frequency domains indicates that in the mid-troposphere the primary contribution to the nonlinear interactions always involves the interactions of the spectral domain of concern with the mean zonal flow and the stationary planetary waves. It is also found that except in the domain of low-frequency, eastward-moving cyclone waves the following characteristics are in common. 1) the meridional transport of angular momentum is directed toward the north pole; 2) the resultant of the nonlinear interactions due to the longitudinal convergence of the transport provides a poleward flux of angular momentum in the domains of eastward-moving waves, but provides an equatorward transport in the domains of westward-moving waves; 3) the resultant of the nonlinear interactions due to the latitudinal convergence of the transport generally contributes a poleward transport of angular momentum in the domains of westward-moving waves, but contributes an equatorward transport in the domains of eastward-moving waves; 4) the ageostrophic effect always counteracts the nonlinear interactions due to the longitudinal convergence of the transport of angular momentum; and 5) the effects of eddy and molecular stress forces generally work against the ageostrophic effect.

The frequency spectra of the meridional transport of angular momentum indicate that: 1) in the summer most of the transport is accomplished by the moving waves, the eastward-moving waves contributing to most of the poleward transport, and the westward-moving waves to the equatorward transport; 2) in the winter most of the transport is accomplished by the stationary waves, and both the eastward- and westward- moving waves contribute to the poleward transport of angular momentum.

The wavenumber spectra of the transport of angular momentum indicate that in both the summer and winter seasons waves of practically all wavelengths in low and middle latitudes contribute to the poleward transport of angular momentum. In high latitudes, however, only the very long waves contribute to the equatorward transport of angular momentum.

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