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

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

2011-04-03

arxiv.org/abs/1104.0404v2

Nonlinear Sciences

Chaotic Dynamics

7 pages, 2 figures, second version, comments welcome!

Scientific paper

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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