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Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere
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Image of FIG. 1.
FIG. 1.

Diagram of relation (38): the coordinate system rotates with respect to the planet about the vector . As a result, the vector , which is steady with respect to the planet, is observed to trace a circular path with respect to the coordinate system.

Image of FIG. 2.
FIG. 2.

Longitudinal velocities as a function of time (days) of, from top to bottom, a cyclogeostrophic cyclone, a geostrophic cyclone, a geostrophic anticyclone, and a cyclogeostrophic anticyclone. All these vortices had a Gaussian profile and obey the full angular momentum equations (48)–(50). Spatially the vortices oscillate about a fixed latitude, in this case about , while drifting westward.

Image of FIG. 3.
FIG. 3.

Trajectories of several geostrophic anticyclones as found by numerical integration. At the vortices are released at several latitudes near . They also have different initial longitudinal velocities. The vortex that starts at 30° has initial velocity as given by Eq. (63). Overall the vortices have initial velocities , where, from bottom to top, .

Image of FIG. 4.
FIG. 4.

The dimensionless drift speed [solution of Eq. (77)] of monopoles as a function of geographical latitude for various modes: slow regular monopoles (sr), slow irregular anticyclones (si), fast regular monopoles (fr), and fast irregular anticyclones (fi)

Image of FIG. 5.
FIG. 5.

Angular momentum diagram for an anticyclonic monopole showing the mechanism of retrograde drift. The encircled cross symbols represent vectors perpendicular to, and into, the plane of the paper.

Image of FIG. 6.
FIG. 6.

Angular momentum diagram for a cyclonic monopole, showing that cyclones, too, drift in retrograde direction (westward). The encircled dot symbols represent vectors perpendicular to the plane of the paper and in the direction toward the reader.


Generic image for table
Table I.

Local inner products are encountered during the evaluation of Eq. (40).

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Table II.

Turning senses (top views and signs), signs of mass anomalies , and the resulting signs of the ratio of these quantities, for cyclones (C) and regular and irregular anticyclones on the northern and southern hemispheres.

Generic image for table
Table III.

Correspondence of branches of Fig. 4 and the parameters and of Eq. (79).

Generic image for table
Table IV.

The nonvanishing components of the metric and nonvanishing Christoffel symbols of spherical coordinate system (E3).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere