We use RWC to diagnose and understand an idealized GCM using the GCM's convergence of the vertical EP flux in the upper troposphere as the wave activity source. The RWC model reproduces the important features of the mean momentum fluxes of the GCM and the responses of the momentum fluxes to poleward shifted jets in response to changes in friction, pole-to-equator temperature gradient, tropopause height, radiative relaxation time scale or tropical static stability. We then use the RWC model to separate the contributions of the source magnitude, the source phase speed and the background flow (with no changes in source) to the momentum flux changes. We find that (1) changes in the background flow (i.e. index of refraction) are responsible for maintaining the poleward shifted jet, (2) source phase speed changes directly oppose the poleward shifted jet and (3) source magnitude changes act to strengthen the mean jet (except in the experiment where only the zonal-mean part of friction is changed, in which case the effect is essentially zero).
The background flow affects the waves via a selective "reflecting level" on poleward flank of jet: for a given wavenumber, low phase speed waves are reflected but high phase speed waves are absorbed at the critical level on the poleward flank of jet. When the zonal-mean zonal wind (U) increases on the poleward flank of the jet, a wider range of poleward propagating waves encounter a reflecting level instead of a critical level on the poleward flank. The increased wave reflection leads to increased equatorward propagating waves (and therefore poleward momentum flux) across the jet.
In the literature, ideas on the effect of phase speed changes on momentum fluxes emphasize the equatorward propagating waves and the critical level on the equatorward flank: an increase in wave phase speed causes the equator-side critical line to move poleward and therefore reduces momentum fluxes on the equatorward flank of the jet. This leads to negative U forcing directly equatorward of the jet and positive forcing deeper in the subtropics. In the presence of a selective reflecting level, however, higher phase speeds also imply more wave absorption and less wave reflection on the poleward flank of the jet. The net result is a reduction in momentum fluxes across the jet in addition to the reduction on the equatorward flank. This also means that the negative U forcing from phase speed changes is actually on the poleward flank of the jet and therefore directly opposes the poleward shift.
The above results show that given a poleward shifted jet, RWC can explain the changes in momentum flux. To understand the response to a stronger jet, we couple the RWC model to (a one layer version of) U and a simple model of the phase speed changes of the wave activity source. The RWC model successfully simulates the poleward shift in response to reduced friction. These experiments also demonstrate that in some cases the changes in source magnitude are essential for acting to strengthen the jet so that the reflecting level dynamics can play a role. In these cases, U will simply increase on the equatorward flank of the jet in the absence the source magnitude feedback (for example, the direct "radiative" response to increased pole-to-equator temperature gradient is predominantly increased U in the subtropics).
We also run a series of RWC experiments with imposed U monopoles at different latitudes. We find that the eddies reinforce the imposed U when it is collocated with the centers of action of EOF1 of the GCM. Reflecting level dynamics are essential for the positive feedback when U is poleward of the jet and critical level dynamics (that are independent of phase speed changes) are essential for the positive feedback when U is equatorward of the jet. When the imposed U is out of phase with EOF1, the eddies tend to shift the imposed U poleward (equatorward) for anomalies that are equatorward (poleward) of 50 degrees. We provide a simple model of critical level dynamics that explains the degree of poleward propagation versus positive feedback in this series of experiments. Also, there is no "baroclinic feedback" in these experiments.
Looking at the imposed U experiments as a whole, we find that all of the dramatic changes in the structure of the momentum fluxes that occur as one changes the U latitude are due to changes in background flow. The changes in momentum fluxes due to changes in phase speed, on the other hand, always have the same broad monopole structure that gradually changes in amplitude as the U latitude changes. This lack of structure occurs because (1) the phase speed changes tend to be non-local in phase speed and (2) the mean wave source phase speed spectrum is broad. For example, suppose that a localized U increases the phase speeds of the wave activity sources in a localized latitude band. Because phase speed changes are nonlocal in phase speed (i.e. high phase speed waves accelerate about as much as low phase speed waves), the changes in wave dissipation and propagation are distributed across all latitudes that have critical and reflecting levels for the waves sources in the latitude band and will therefore be broad and non-local.