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| Titel |
On the advection in the flow field generated by near stationary structures of three vorticies in a two-layer rotating fluid |
| VerfasserIn |
Konstantin Koshel, Michail Sokolovskiy, Jacques Verron |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250031714
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| Zusammenfassung |
| In a two-layer quasi-geostrophic model, the evolution of a symmetric baroclinic tripole,
composed of a central vortex with strength μκ in the upper layer, and two satellites with
strength κ in the lower layer, is studied. The equation
F(B, R; μ) =-1-+-2R(1+-μ)-+K1 (2R )+ (2R-+-Bμ)K1-(2R---B-)--[2R-(1-+-μ)--Bμ-]K1-(B-)= 0,
2R B (2R- B ) 2(R - B)
give a uniform rotation of this collinear configuration with a constant angular velocity
[ ]
Ï = -γ-κ(μ-+-2)-- B-+-2Rμ-- μK1(B )+ K1(2R)
4Ï(2R + Bμ) 2BR
with respect to the center of vorticity with coordinates
(Xc, Yc) = (2(R - B )-(μ + 2), 0).
Here the B is distance from one lower layer vortex to upper layer vortex and 2R is distance
between lower layer vortexes. At μ = -2 the angular velocity has identically zero value, the
center of vorticity Xc shifts to the infinitely remote point, and the equation takes a
form
B2 --2BR-+-4R2-
F(B, R) = 2BR (2R- B ) - K1 (B)- K1 (2R - B )- K1(2R) = 0,
and the collinear vortex structure performs a rectilinear motion with a constant
velocity
[ ]
κγ- -2(R---B)-
V = 4Ï B (2R - B ) - K1 (B )+ K1(2R - B)
in the direction, normal to the axis x.
In our work, we discuss the problem of the advection of fluid particles in the velocity field
induced by these three-vortex two-layer stationary structures. More detailed analysis of the
phase portraits of water motion, induced by collinear structures, and the analysis of the
perturbed motion and the conditions of the chaotic regime appearance will be given in the
talk. For analysis of chaotic regime appearance condition we will use method of unperturbed
rotation frequency and nonlinear resonances investigation proposed in work Koshel K.V.,
Sokolovskiy M.A., Davies P.A., 2008. Chaotic advection and nonlinear resonances in a
periodic flow above submerged obstacle. Fluid dynamics research, 40, 695–736. |
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