Progress in the rapidly expanding exploration of planetary atmospheric and oceanic environments demands an adequate qualitative and quantitative representation of various processes in anisotropic turbulence. The existing analytical spectral theories are developed for homogeneous isotropic flows. They quickly become very complicated when expanded to anisotropic flows with waves. It is possible, however, to extend one such theory, the quasinormal scale elimination (QNSE), to stably stratified and rotating flows. Here the results of the theory are compared with a large variety of oceanic and atmospheric flows. These comparisons make it possible to clarify the physics of some processes governing the atmospheric and oceanic dynamics, quantify their spectra, and investigate their latitudinal and longitudinal variabilities. Some of the main results of this analysis are that vertical and horizontal spectra of atmospheric and oceanic turbulence can be derived within QNSE analytically; there exists a quantitative affinity between atmospheric and oceanic spectra; on large scales, spectral amplitudes are determined by the extra strains that cause flow anisotropization, rather than the energy or enstrophy fluxes; and planetary circulations appear to be amenable to classification as flows with compactified (compressed) dimensionality.