Figure 1

Evolution of thickness during relaxation of the QG modon with $\mathrm{Ro}=0.4$. From left to right and top to bottom: $t=0$, 6, 12, and 24 (units of $f^{-1}$). The thickness anomaly is given at the interval 0.06 in units of $H_0$. Black: cyclone (depression), gray: anticyclone. Thin dotted line indicates zero thickness anomaly.Reuse & Permissions

Figure 2

Evolution of the PV anomaly corresponding to Fig. 1. Values from $\pm 0.1$ [respectively in black ($+$) and gray ($-$)] at the interval 1 up to 10.1 and then at the interval 5 (suitable for cyclone only), in units of $\frac{f}{H_0}$.Reuse & Permissions

Figure 3

Isobars with superimposed velocity field (left), PV anomaly (middle), and divergence (right) of the modon at $t=46$. Same legend as in Figs. 1, 2 for the left and middle panels. Thin lines are added at values $\pm 0.5$ for the PV anomaly. Thin black dotted lines in the right panel indicate PV anomaly $q_A=\pm 0.1$ contours roughly corresponding to the dipole’s edge. Absolute value of divergence in units of $f$: levels of gray from 0.1 (white) to 4 (black); Limits of convergence (divergence) zones: black (gray) contours.Reuse & Permissions

Figure 4

$|\mathbf{v}|/\sqrt{g{H}_0}$ (Froude number, black line) , thickness $h+0.3$ (dashed line), and divergence $\nabla ·\mathbf{v}$ (gray line) profiles along the modon’s axis at $t=46$.Reuse & Permissions

Figure 5

Upper panel: kinetic (gray) and potential (black) energy during the evolution of a shock modon. Lower panel: total energy (continuous line) and energy dissipation (crosses).Reuse & Permissions

Figure 6

Modon trajectory from $t=40$ to $t=460$. Color switches from black to gray when the shock vanishes. Time interval: 5.Reuse & Permissions

Figure 7

Bernoulli function vs PV for the shock modon at $t=46$.Reuse & Permissions

Figure 8

Isobars with superimposed velocity field (left) and potential vorticity anomaly (right) of the “shock tripole” formed after the collision of two shock modons. Same legend as in Figs. 1, 2.Reuse & Permissions