Abstract/Details

Minimax variational principle for the rotating shallow water equations: First order Rossby number effects in geophysical flows


2006 2006

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Abstract (summary)

We show that physically interesting steady states of the Rotating Shallow Water equations are characterized by a minimax principle. The objective functional is A-&thetas;H where A is the quadratic enstrophy, H is the energy and &thetas; is a positive constant. The inner maximization is subject to a pointwise constraint on the potential vorticity (PV) while the outer minimization is over all vorticity fields. In physical terms, the inner maximization represents geostrophic adjustment, while the outer minimization represents relaxation to a steady state through PV mixing. The key idea behind the principle is the separation of time scales between the fast inertial-gravity waves and the slow vortical modes, which implies that during geostrophic adjustment, the vorticity field remains frozen, while during vortical mixing the energy remains constant. The inner maximization problem is solved analytically by an asymptotic expansion in Rossby number ε, thus obtaining a first order correction to the quasigeostrophic(QG) fields. The outer minimization problem is then solved numerically for the 1-D case using the corrected fields. The resulting steady flows are therefore analogues of quasigeostrophic steady states at finite ε.

The first order Rossby number effect is examined for zonal shear flows in parameter regimes relevant to the oceans and to the atmosphere of Jupiter, and include the β effect and bottom topography. Some of the striking results at finite Rossby number include the cyclone-anticyclone asymmetry, when anticyclones are found to be much more prevalent than cyclones. Also as an example, for two different bands on Jupiter, certain jet structures are found be more robust than others when first order Rossby number corrections are included.

Indexing (details)


Subject
Geophysics;
Mathematics
Classification
0373: Geophysics
0405: Mathematics
Identifier / keyword
Pure sciences, Earth sciences, Geophysical flows, Minimax, Rossby number, Rotating shallow water equations
Title
Minimax variational principle for the rotating shallow water equations: First order Rossby number effects in geophysical flows
Author
Nageswaran, Visweswaran
Number of pages
97
Publication year
2006
Degree date
2006
School code
0118
Source
DAI-B 67/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542982217
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
3242107
ProQuest document ID
305308900
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305308900
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