On nonlinear cascades of atmospheric energy and enstrophy in a two-dimensional spectral index

Diagnostic analyses of the spectra and nonlinear exchange of the kinetic energy (K), enstrophy (E), and available potential energy (A) are made using the degree of the Legendre polynomial expansion, n, as a two-dimensional spectral index. Results are presented for a data set covering the period from December 19, 1971 to February 27, 1972. The spectra of K, E, and A have slopes close to -3, -1, and -3, respectively for large n. K and E cascade nonlinearly from the scales of intermediate n to the scales of large and small n. A cascades from n = 1 and 2, particularly the latter, to scales with larger n. The fluxes of nonlinear exchanges of K, E, and A are also evaluated to investigate if an inertial subrange exists. No firm conclusion for the existence of this subrange can be made.