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Statistical mechanics of a finite difference approximation to the barotropic vorticity equation
Author(s) -
Bennett A. F.,
Middleton J. F.
Publication year - 1983
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710946208
Subject(s) - barotropic fluid , wavenumber , vorticity , isotropy , finite difference , fourier transform , jacobian matrix and determinant , mathematics , amplitude , mathematical analysis , predictability , finite difference method , physics , statistical physics , classical mechanics , vortex , mechanics , quantum mechanics , statistics
A conventional finite‐difference representation of the barotropic vorticity equation is shown to possess a statistical mechanical equilibrium state, which is attained as a quasi‐equilibrium in the presence of weak dissipation. The state is isotropic only in suitably chosen wavenumber coordinates. The autocorrelation functions of the discrete complex Fourier amplitudes have integral time scales which are O(wave number) −1 at middle wavenumber, but which are infinite at the highest wavenumbers. This is demonstrated experimentally and confirmed by inspection of the interaction coefficients for the finite‐difference Jacobian. The results emphasize the dependence of predictability upon the choice of numerical method.