## Abstract

The growth rate of baroclinic instability waves is generalized in terms of wave–mean flow interactions, with an emphasis on the influence of the vertical profile of baroclinicity. The wave energy is converted from the zonal mean kinetic energy and the growth rate is proportional to the mean zonal flow difference between the Eliassen–Palm (E-P) flux convergence and divergence areas. Mass-weighted isentropic zonal means facilitate the expression of the lower boundary conditions for the mass streamfunctions and E-P flux.

For Eady waves, intersections of isentropes with lower/upper boundaries induce the E-P flux divergence/convergence. The growth rate is proportional to the mean zonal flow difference between the two boundaries, indicating that baroclinicity at each level contributes evenly to the instability. The reduced zonal mean kinetic energy is compensated by a conversion from the zonal mean available potential energy.

Aquaplanet experiments are carried out to investigate the actual characteristics of baroclinic instability waves. The wave activity is shown to be sensitive to the upper-tropospheric baroclinicity, though it may be most sensitive to baroclinicity near 800 hPa, which is the maximal level of the E-P flux. The local wave energy generation rate suggests that the increased upper-tropospheric zonal flow directly enhances the upper-tropospheric wave energy at the midlatitudes. Note that the actual baroclinic instability waves accompany a considerable amount of the equatorward E-P flux, which causes extinction of wave energy in the subtropical upper troposphere.

*Corresponding author address:*Toshiki Iwasaki, Graduate School of Science, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8578, Japan. E-mail: iwasaki@wind.gp.tohoku.ac.jp