Low-Frequency Equatorial Waves in Vertically Sheared Zonal Flow. Part II: Unstable Waves

Abstract

The stability of equatorial Rossby waves in the presence of mean flow vertical shear and moisture convergence-induced heating is investigated with a primitive equation model on an equatorial ? plane. A vertical shear alone can destabilize equatorial Rossby waves by feeding mean flow available potential energy to the waves. This energy transfer necessitates unstable waves? constant phase lines tilt both horizontally (eastward with latitude) and vertically (against the shear). The preferred most unstable wavelength increases with increasing vertical shear and with decreasing heating intensity, ranging typically from 3000 to 5000 km. The instability strongly depends on meridional variation of the vertical shear. A broader meridional extent of the shear allows a faster growth and a less-trapped meridional structure. When the shear is asymmetric relative to the equator, the unstable Rossby wave is constrained to the hemisphere where the shear is prominent. Without boundary layer friction the Rossby wave instability does not depend on the sign of the vertical shear, whereas in the presence of the boundary layer, the moist Rossby wave instability is remarkably enhanced (suppressed) by easterly (westerly) vertical shears. This results from the fact that an easterly shear confines the wave to the lower level, generating a stronger Ekman-pumping-induced heating and an enhanced meridional heat flux, both of which reinforce the instability. The moist baroclinic instability is a mechanism by which westward propagating rotational waves (Rossby and Yanai waves) can be destabilized, whereas Kelvin waves cannot. This is because the transfer of mean potential energy to eddy requires significant magnitude of barotropic motion. The latter is a modified Rossby wave and can be resonantly excited only by the westward propagating rotational waves. The common features and differences of the equatorial Rossby wave instability and midlatitude baroclinic instability, as well as the implications of the results are discussed.