The effects of variations in jet width on the downstream growth of baroclinic waves are studied, using a simple quasigeostrophic model with a vertically varying basic state and variable channel width, as well as a simplified primitive equation model with a basic state that varies in latitude and height. This study is motivated by observations that in midwinter in the Pacific the storm track is weaker and the jet is narrower during years when the jet is strong.The linear models are able to reproduce the observed decrease of spatial growth rate with shear, if the narrowing of the jet is accounted for by assuming it decreases the meridional wavelength of the perturbations, which hampers their growth. A common suggestion has been that perturbations are weaker when the jet is strong because they move faster out of the unstable storm track region. The authors find that one needs to take into account that the jet narrows when it strengthens; otherwise, the increase of growth rate is strong enough to counteract the effect of increased advection speed.It is also found that, when the model basic state is Eady-like ( small or zero meridional potential vorticity gradients in the troposphere), the short-wave cutoff for instability moves to large-scale waves as shear is increased, due to the accompanying increase in meridional wavenumber. This results in a transition from a regime where upper-level perturbations spin up a surface circulation very rapidly, and normal-mode growth ensues, to a regime where the initial perturbations take a very long time to excite growth. Since waves slow down when a surface perturbation develops, this can explain the observations that the storm track perturbations are more "upper level'' during strong jet years and their group velocities increase faster than linearly with shear.
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