Smooth semianalytical multipole solutions on the rigid-lid -plane. (a) Tripole ; (b) quadrupole ; (c) pentapole ; (d) hexapole ; (e) heptapole . Left column, stream-function contours in a corotating frame of reference; central column, cross section of the vorticity fields along the dashed line shown in the left-column panel; right column, scatter graph—the computed vorticity–stream-function relation. All variables are nondimensional; stream-function contours are given at a 0.25 step. Straight lines in the scatter graphs represent the vs relation outside the separatrix; curved lines, same in the interior region.
Form characteristics of a smooth two-mode -pole on the rigid-lid -plane as functions of . Black bars, to ratio ( and are the maximal and minimal separatrix radii); white bars, ratio of the core-vortex area to the total area of satellites.
Relation between and on the equivalent-barotropic -plane at a fixed ; , .
The minimal separatrix radius, , and the ratio of the maximal radius, , to as functions of and in a unimodal multipole. (a) ; (b) . Indices indicate the values of to which the graphs correspond.
The minimal separatrix radius, , and the ratio of the maximal radius, , to as functions of and in a smooth two-mode multipole. (a) ; (b) . Notations as in Fig. 4 .
Smooth semianalytical two-mode tripole solutions at different values of in the rigid-lid -plane and equivalent-barotropic -plane models. (a) ; (b) ; (c) . Left column, stream-function contours in the corotating frame of reference; central column, cross section of the potential vorticity field, , along the axis on a rigid-lid -plane ; right column, cross section of the absolute vorticity field, , along the axis on the equivalent-barotropic -plane . Notations as in Fig. 1 .
Smooth semianalytical multipole solutions on the rigid-lid -plane at . (a) Quadrupole ; (b) pentapole ; (c) hexapole ; (d) heptapole . Notations as in Fig. 1 .
Smooth semianalytical clockwise-rotating tripoles on the equivalent-barotropic -plane at . (a) , i.e., and ; (b) , i.e., and . Notations as in Fig. 1 .
Accuracy estimates for smooth two-mode multipoles on a rigid-lid -plane at the output of the iterative procedure. Root-mean-square and maximal residuals in Eq. (21) and boundary conditions (22) computed over the interior and boundary grid points, respectively. , multipole order; , polynomial power.
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