On anomalous meridional circulations and Eliassen-Palm flux divergences in an idealized model of dissipating, non-breaking Rossby waves

Abstract

Even in idealized models of steady, dissipating, non-breaking Rossby waves at small wave amplitude, and even in the absence of barotropic and baroclinic shear instabilities, there can be an anomalous Eliassen-Palm flux divergence in the sense that the divergence is positive when the background potential-vorticity gradient is also positive, implying upgradient eddy potential-vorticity transport. The phenomenon is illustrated in the simplest possible case of dissipation by Rayleigh friction and Newtonian cooling, and is shown by a more general argument not to be restricted to that case. The physical reason is that infrared radiative damping can act anti-dissipatively on potential-vorticity anomalies whenever the vertical disturbance structure is diffractive or evanescent, as with most real stratospheric synoptic and sub-synoptic-scale disturbances forced from below. Associated with this phenomenon are anomalous (eastward) phase tilts with height, and equatorward transformed Eulerian-mean (TEM) meridional velocities. It is pointed out that the latter is a clearcut example of a TEM circulation whose sense is opposite to that of the generalized Lagrangian-mean circulation (and the effective transport circulation in the sense of Plumb and Mahlman) induced by the same steady, small-amplitude disturbance.