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Noncoincidence of separatrices in two-layer modons
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10.1063/1.2731741
/content/aip/journal/pof2/19/5/10.1063/1.2731741
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/5/10.1063/1.2731741

Figures

Image of FIG. 1.
FIG. 1.

Upper- and lower-layer separatrices in two-layer vortical pairs: (a) -plane distributed modon equilibrium achieved in a numerical simulation (see text for details); (b) typical separatrices of an -plane heton translating in the direction. Solid closed line, upper layer; dashed line, lower layer.

Image of FIG. 2.
FIG. 2.

Notations: domains , , , and , and separatrices and . Solid closed line, upper layer; dashed line, lower layer.

Image of FIG. 3.
FIG. 3.

Domains and , their boundaries and , and schematic of the numerical grid.

Image of FIG. 4.
FIG. 4.

PV jump across the separatrix in the upper layer, , as a function of . -plane modons with , , and ; (a) general view with two roots 1 and 2; (b) magnified graph in the vicinity of root 1; (c) same in the vicinity of root 2.

Image of FIG. 5.
FIG. 5.

The -plane modon given by the parameters , , , and (root 2). (a) and (b) Upper-layer contours of the comoving streamfunction and potential vorticity , respectively; (c) separatrices (solid line) and (dashed line); (d) and (e) cross sections along the axis of and , respectively; (f) vs scatter-graph. In (a) and (b), the contour interval is 10% of the maximum; dotted line is the separatrix ; shaded, regions of positive values and .

Image of FIG. 6.
FIG. 6.

The -plane modon given by the parameters , , , and (root 1). Notations as in Fig. 5.

Image of FIG. 7.
FIG. 7.

The supersmooth -plane modon solution given by the parameters , , , and . (a)–(f) As in Fig. 5; inset in (f), magnified view of vs scatter-graph in the vicinity of the point of contact .

Image of FIG. 8.
FIG. 8.

The -plane modon equilibrium achieved in a numerical simulation with time integration from an unsteady initial state [Fig. 1(a)]. Notations as in Fig. 5.

Image of FIG. 9.
FIG. 9.

Evolution of the supersmooth modon (Fig. 7) in two simulations. (a)–(c) Under perturbations caused by the numerical procedure only (including the cutting filter); (d)–(f) tilted modon. (a) and (d) in the initial states; (b) and (e) at ; (c) and (f) vs scatter graphs at .

Image of FIG. 10.
FIG. 10.

First simulation: modon characteristics at . Notations as in Fig. 5. Changes from to are fairly small.

Image of FIG. 11.
FIG. 11.

Second simulation: transition to a nonoverlapping state. (a) Separation between the upper- and lower-layer PV peaks vs time; (b) -component, , of the modon speed vs time.

Image of FIG. 12.
FIG. 12.

Second simulation: modon characteristics at . Notations as in Fig. 5. The overlap of the upper and lower PV chunks is negligible.

Image of FIG. 13.
FIG. 13.

The supersmooth -plane modon solution given by the parameters , , , and . Notations as in Fig. 7; black area in (b), zero .

Tables

Generic image for table
Table I.

Maximal difference between and , and difference between and , as functions of shift . The external parameters used are , , and .

Generic image for table
Table II.

Accuracy of the interior solution: root-mean-square (RMS) and maximal (Max) residuals. Two left columns, Eqs. (29) and (30); two right columns, Eqs. (29) and (31).

Generic image for table
Table III.

Accuracy estimates for matching of the layer streamfunctions and their derivatives at and : RMS and maximal residuals. Four left columns, conditions (33), two right columns, conditions (34).

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/content/aip/journal/pof2/19/5/10.1063/1.2731741
2007-05-17
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Noncoincidence of separatrices in two-layer modons
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/5/10.1063/1.2731741
10.1063/1.2731741
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