A note on baroclinic solitary waves with radial symmetry

Swenson, Mark

doi:10.1016/0377-0265(86)90015-1

Cited by 3 publications

(2 citation statements)

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“…Swenson [ 13 ] derives a first order eigencondition similar to (3.8) when refining Flierl's theory [11] of quasi-geostrophic solitary waves in a weak shear flow. In that model, however, the integral contains only a single term and there is no parameter to 10 05 / -..…”

Section: Monopoles In the Variable Coefficient Aew: Perturbation Theomentioning

confidence: 99%

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Monopolar and dipolar vortex solitons in two space dimensions

Boyd

1991

Wave Motion

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We compute solitary waves which solve Au _y2 U-(U +yu2)/C = 0 where c is the phase speed in the x direction and y = 0 is the equator. This equation is a heuristic model for Rossby waves on the "equatorial beta-plane" in geophysical fluid dynamics. For positive c only, there are one-signed solutions ("monopole vortices") which are centered in the middle latitudes. When c c [-oG-1/3] or c > 0, there are dipoles which have matching vortices of opposite sign in each hemisphere. A third class of solutions is composed of equator-spanning monopoles that are unsymmetric in y. In addition to these families of strict solitary waves, there are also quadrapole vortices which are "weakly non-local solitons" in the sense that they almost meet the usual criterion for solitary waves except for a weak-very weak-radiation to infinity. Orthogonal rational Chebyshev functions and Newton's iteration are used to compute numerical solutions, but four analytic approximations are also derived. Although the equation is only a crude model of geophysical waves, its rich diversity offers a good education in solitary waves in two space dimensions.

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Section: Monopoles In the Variable Coefficient Aew: Perturbation Theomentioning

confidence: 99%

“…Flierl's quasi-geostrophic model replaces the Coriolis parameter by a constant but has y-varying terms because of the mean current. Swenson [13] showed that this leads to a contradiction at perturbative first order. In our model, the Coriolis parameter is allowed to vary, and monopoles exist.…”

Section: J(a B) = Ab -Ab (A5)mentioning

confidence: 99%