= Solution
For a zonal background $U(y)$, its <relative vorticity> is $\overline\xi=-U_y$. The meridional <absolute vorticity> gradient is therefore
$$
Q_y=\beta-U_{yy},\qquad
\beta=\frac{2\Omega\cos\phi}{a}.
$$
At $30^\circ\mathrm N$,
$$
\boxed{\beta\simeq1.98\times10^{-11}\ \mathrm{m^{-1}\,s^{-1}}.}
$$
A localized <jet stream> of <velocity> scale $U=134\ \mathrm{m\,s^{-1}}$ and width $L$ has
$$
\boxed{|\overline\xi_y|=|U_{yy}|\sim\frac U{L^2}
=1.34\times10^{-10}\left(\frac{1000\ \mathrm{km}}L\right)^2
\mathrm{m^{-1}\,s^{-1}}.}
$$
For $L=1000$--$2000\ \mathrm{km}$ this is about $1.7$--$6.8$ times the planetary contribution, so wind curvature cannot generally be neglected. The coefficient in this scaling depends on the chosen jet profile and width convention.
Linearizing the <vorticity equation> now gives the <Rossby-wave equation for a sheared zonal current>
$$
(\partial_t+U(y)\partial_x)\nabla_h^2\psi+(\beta-U_{yy})\psi_x=0.
$$
For a qualitative estimate at the jet core, freeze the local coefficients. At a smooth maximum $U_{yy}<0$, so $Q_y>\beta$: the restoring <absolute vorticity> gradient is stronger. The <local Rossby-wave dispersion relation in a zonal jet> gives, for the same local $U$ and zonal <wavenumber> $k$ with $l=0$,
$$
c_p=U-\frac{Q_y}{k^2},\qquad c_g=U+\frac{Q_y}{k^2},
$$
so
$$
\boxed{\Delta c_p=\frac{U_{yy}}{k^2}<0,\qquad
\Delta c_g=-\frac{U_{yy}}{k^2}>0.}
$$
The envelope in the diagram would advance eastward faster, while individual phase contours would advance more slowly eastward, become stationary if $Q_y=Uk^2$, or move westward if $Q_y>Uk^2$. The separation between envelope and phase speeds increases. On a plot with time downward, compare horizontal displacement at fixed time: the envelope moves farther right, while a given phase moves less far right, or left after reversal. If the <frequency> changes sign for a fixed signed $k$, conjugate the mode to restore the convention $\omega\geq0$; the physical propagation is unchanged.
This conclusion concerns the concave-down jet core. On a flank with $U_{yy}>0$ the correction has the opposite sign; the value at the edge of the <Hadley cell> alone does not specify the curvature everywhere. Indeed the angular-momentum-conserving profile in 1(a) is a rising inner branch, not a complete smooth jet maximum. A global sheared-current <normal mode> requires its meridional structure and boundary conditions; the local calculation is the qualitative estimate requested.
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