Enstrophy bounds and the range of space-time scales in the hydrostatic primitive equations

2011/04/03 by John Gibbon, Darryl D. Holm, Gibbon, J. D. +1
Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Meteorological Phenomena and Simulations #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes

paper · pdf · doi:10.48550/arxiv.1104.0404

openalex publication_date 2011/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The hydrostatic primitive equations (HPE) form the basis of most numerical weather, climate and global ocean circulation models. Analytical (not statistical) methods are used to find a scaling proportional to (Nu Ra Re)^1/4 for the range of horizontal spatial sizes in HPE solutions, which is much broader than currently achievable computationally. The range of scales for the HPE is determined from an analytical bound on the time-averaged enstrophy of the horizontal circulation. This bound allows the formation of very small spatial scales, whose existence would excite unphysically large linear oscillation frequencies and gravity wave speeds.

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