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Fig. 9.

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Instability diagram showing the resistive wavenumber, kη, as a function of the stratification wavenumber, kN, both scaled by the shell gap, D. Individual simulation runs are represented by symbols: crosses indicate decaying nonaxisymmetric perturbations, while circles and triangles mark unstable global and WKB-type m = 1 modes, respectively. The symbol color codes the instability growth rate σ. The shaded gray and blue regions denote the stable regime and the global mode regime, respectively, based on the simulation data. The boundaries of these shaded regions are defined by Eq. (43) (stability line) and Eq. (44) (transition line between the global and WKB regimes). Thin dotted horizontal and vertical rectangles highlight runs in subset 1 ( Lu ¯ 1 680 $ \overline{\mathrm{Lu}}_1\approx 680 $) and subset 2 ( δ ¯ 1 = 180 $ \overline{\delta}_1=180 $).

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