On the Effect of Surface Friction and Upward Radiation of Energy on Equatorial Waves

Abstract

In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax the rigid-lid assumption and impose surface drag, which allows the barotropic mode to be excited in equatorial waves. In particular, a previously developed set of linear, strict quasi-equilibrium tropospheric equations is coupled with a dry, passive stratosphere, and surface drag is added to the troposphere momentum equations. Theoretical and numerical model analysis is performed on the model in the limits of an inviscid surface coupled to a stratosphere, as well as a frictional surface under a rigid-lid. This study confirms previous research that shows the presence of a stratosphere strongly shifts the growth rates of fast propagating equatorial waves to larger scales, reddening the equatorial power spectrum. The growth rates of modes that are slowly propagating and highly interactive with cloud-radiation are shown to be negligibly affected by the presence of a stratosphere. Surface friction in this model framework acts as purely a damping mechanism and increases the poleward extent of the equatorial waves through barotropic vorticity generation. Numerical solutions of the coupled troposphere-stratosphere model with surface friction also show that the barotropic mode can be tropospherically trapped when excited by surface friction but in the presence of a highly stratified stratosphere. The superposition of phase-shifted barotropic and first baroclinic modes is also shown to lead to an eastward vertical tilt in the dynamical fields of Kelvin-wave like modes.