 Solution

For a zonal background $U(y)$, its relative vorticity is $\overline{\xi }=-U_y$. The meridional absolute vorticity gradient is thereforeAt $30^{\circ }\mathrm{N}$,A localized jet stream of velocity scale $U=134\mathrm{m}{\mathrm{s}}^{-1}$ and width $L$ hasFor $L=1000$--$2000\mathrm{km}$ 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 currentFor 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 $l=0$,soThe envelope in the diagram would advance eastward faster, while individual phase contours would advance more slowly eastward, become stationary if $Q_y=U{k}^2$, or move westward if $Q_y>U{k}^2$. 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 $\omega \ge 0$; 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.