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Spontaneous Imbalance and Hybrid Vortex–Gravity Structures - page 6 / 12





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FIG. 1. Rightward-propagating 3D vortex dipoles shown by vertical and horizontal sections representing the two best-resolved cases in (top) S07 and in (bottom) V06, V07, and V08 (from V07). The vertical sections on the left are taken along the heavy straight lines seen in the horizontal sections on the right. The gray shading in each panel shows the omega or vertical velocity field, which oscillates around zero with signs indicated by the white arrows. The vertical section at bottom left shows the bottom half, z , 0, of the dipole described in V07. The heavy horizontal lines mark depths z with nominal values 20.21, 20.9 in the dimensionless units used in V07. The horizontal section at bottom right is at z 5 20.9, and at top right is at z 5 0.25 km. The vertical section at bottom left has been expanded vertically so as to agree with the coordinate aspect ratio of the section at top left after scaling by Prandtl’s ratio N/f, whose value at top left is 100 (5 200 km/2 km). Further detail can be seen in S07’s Figs. 10 and 11 and in V07’s Figs. 1–4 and 11–15. In V07’s Fig. 2 the origin of coordinates needs correction: the horizontal midplane of the dipole is at z 5 0. The top half of the dipole is never shown. The three-dimensional PV anomalies in V07’s case occupy the vertical range 21.2 # z # 1.2 approximately. The nominal z values are Boussinesq isopycnal coordinate values defined in terms of the 512 stratification layers used in the numerical discretization, representing continuous stratification to good approximation. The computational domains are larger than shown and are respectively a doubly periodic domain with a sponge lid in S07 and a triply periodic domain in V07. The thin contours at top left mark horizontal rightward flow speeds |v| 5 1, 2, 3,. . ., 7 m s21 in the comoving frame of reference. The faint thick contour marks the separatrix or |v| 5 0 surface. The thin contours in the horizontal section at top right give the surface potential temperature field, the Bretherton PV delta function whose inversion dominates S07’s dipole structure.

here, as shown shortly. However, on closer examination we shall see that it is not a case of master and slave either. Appearances are deceptive in this regard.

Figure 1 summarizes the two best-resolved exam- ples, with vertical sections on the left and horizontal on the right. The top left panel, after S07’s Fig. 9, shows the streamwise vertical midplane for a dipole structure induced mainly by a distribution of poten- tial-temperature anomalies on a solid bottom bound-

ary z 5 0. This is equivalent to a Bretherton PV delta function. The interior PV is isentropically uniform, to a first approximation. The faint thick contour on the right of the top left panel marks the separatrix or |v| 5

  • 0

    isotach in the comoving reference frame, where |v| is

horizontal flow speed. The other contours are the iso- tachs for horizontal rightward flow speeds 1, 2, 3, . . . , 7 m s21 in the comoving frame. The shading shows the omega or vertical velocity field (see caption). The most

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