Statistically Relevant Conserved Quantities for Truncated Quasigeostrophic Flow

Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A scientific debate over more than the last 25 years involves which conserved quantities among the formally...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2003-04, Vol.100 (7), p.3841-3846
Main Authors: Abramov, Rafail V., Majda, Andrew J.
Format: Article
Language:English
Subjects:
Energy
Energy spectrum
Energy value
Mathematical analysis
Physical Sciences
Skewed distribution
Statistical analysis
Statistical relevance model
Statistical theories
Statistics
Stream functions
Truncation
Vorticity
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Summary:Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A scientific debate over more than the last 25 years involves which conserved quantities among the formally infinite list are statistically relevant for the large-scale equilibrium statistical behavior. Here this important issue is addressed by using suitable discrete numerical approximations for geophysical flows with many conserved quantities as a numerical laboratory. The results of numerical experiments are presented here for these truncated geophysical flows with topography in a suitable regime. These experiments establish that the integrated third power of potential vorticity besides the familiar constraints of energy, circulation, and enstrophy (the integrated second power) is statistically relevant in this regime for the coarse-grained equilibrium statistical behavior at large scales. Furthermore, the integrated higher powers of potential vorticity larger than three are statistically irrelevant for the large-scale equilibrium statistical behavior in the examples studied here.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0230451100