Abstract/Details

Undulating coherent structures in two-dimensional turbulence: A quasi -equilibrium approach


2002 2002

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Abstract (summary)

The Great Dark Spot (GDS) on Neptune provides a particularly interesting example of a long-lived, large-scale coherent structure in geostrophic turbulence. This coherent structure exhibits periodic oscillations in the aspect ratio and the orientation with respect to the zonal direction of the GDS. Polvani et al. [25] proposed a simple deterministic model of the GDS as oval vortex patch in shear, having constant values of potential vorticity in the vortex and in the ambient zonal flow. Using an equivalent barotropic, quasi-geostrophic dynamics, they showed that the observed characteristics of GDS oscillation can be reproduced by their simple model. The primary goal of the present paper is to develop a statistical model of the GDS that is analogous to the deterministic model of Polvani et al. In order to take such an approach to model the GDS, which is a slowly-varying coherent structure, it is necessary to extend the statistical equilibrium theory based on exact invariants to a quasi-equilibrium theory, in which some further quasi-invariants constrain the most probable state. For an undulating oval vortex, these quasi-invariants are certain quadratic moments of the potential vorticity anomaly that effectively determine the aspect ratio and orientation of the vortex. We validate our quasi-equilibrium theory by reproducing the Kida ellipse, an undulating elliptical vortex patch that is an exact ideal fluid motion, through our quasi-equilibrium approach. In addition, we find new families of steady oval vortices in two-dimensional and quasi-geostrophic flow. The families of statistical equilibria extend the Moore-Saffman elliptical vortices, which are deterministic steady flows.

Indexing (details)


Subject
Mathematics;
Geophysics;
Astronomy;
Astrophysics
Classification
0405: Mathematics
0373: Geophysics
0606: Astronomy
0606: Astrophysics
Identifier / keyword
Pure sciences, Earth sciences, Coherent structures, Geostrophic, Great Dark Spot, Quasi-equilibrium, Turbulence
Title
Undulating coherent structures in two-dimensional turbulence: A quasi -equilibrium approach
Author
Liang, Zhi
Number of pages
111
Publication year
2002
Degree date
2002
School code
0118
Source
DAI-B 63/01, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780493525938, 0493525939
Advisor
Turkington, Bruce
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3039372
ProQuest document ID
251724035
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/251724035
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