Quasinormal scale elimination theory of the anisotropic energy spectra of atmospheric and oceanic turbulence

Circulations of planetary atmospheres and oceans feature huge Reynolds numbers and are turbulent on almost all scales of motion. In addition, the action of density stratification, planetary rotation, streamline curvature, geometric confinement and other factors render these circulations anisotropic. A systematic description of turbulence behavior in response to the impact exerted by extra strains is one of the important outstanding problems of fluid dynamics. Attempts to address this problem ran into difficulty from the outset due to the proliferation of dimensional variables that hinder the application of dimensional analysis. Moreover, direct numerical simulations are limited by the value of the resolvable Reynolds number, even in relatively simple cases of channel flows. Linear and nonlinear theories of anisotropic turbulence have been proposed over the years, yet a clear understanding of the spectral behavior of such flows remains elusive. Further progress relies upon the development of basic self-consistent theories that make verifiable predictions suitable for testing against a large variety of data.

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 were initially developed for homogeneous isotropic flows. They quickly become very complicated when expanded to anisotropic flows with waves. Nonetheless, it is possible to extend one such theory: i.e. the quasinormal scale elimination (QNSE), to stably stratified and rotating flows.

On this account, Professor Boris Galperin from the University of South Florida, in collaboration with Professor Semion Sukoriansky at the Ben-Gurion University of the Negev in Israel, employed QNSE to analyze on a scale-by-scale basis the interactions between different physical processes, under the assumption of an infinite Reynolds number. Their work is currently published in the research journal, Physical Review Fluids.

In their approach, theoretical predictions of various spectra were compared with measurements in atmospheric and oceanic flows. Particular attention was given to one-dimensional (1D) spectra that quantify the turbulence anisotropy. The researchers were motivated by the realization that in existing literature, there is a lack of clarity with regard to spectral slopes and amplitudes of atmospheric and oceanic turbulence, their dependence on latitude, and generally their governing physics.

The authors reported that vertical and horizontal spectra of atmospheric and oceanic turbulence could be derived within QNSE analytically and, furthermore, there exists a quantitative affinity between atmospheric and oceanic spectra. They established that on large scales, spectral amplitudes are likely determined by the extra strains that cause flow anisotropization, rather than the energy or enstrophy fluxes. Overall, planetary circulations were reported to appear to be amenable to classification as flows with compactified (compressed) dimensionality.

By comparing the results of the QNSE theory with a large number of oceanic and atmospheric flows, Galperin and Sukoriansky were not only able to clarify processes governing the atmospheric and oceanic dynamics, but also to quantify their spectral characteristics, including latitudinal, longitudinal and seasonal variabilities. When generalized for spherical coordinates, the QNSE results were in good agreement with numerical simulations, replicated the well-known but poorly understood Nastrom-Gage spectra in the spherical geometry, and provided guidelines for deriving the subgrid-scale parametrizations suitable for implementation in numerical models. In a statement to Advances in Engineering, Professor Boris Galperin highlighted that despite large differences in visual appearances of the atmospheric and oceanic circulations, their spectra are remarkably congruent. This important property of the spectra is accurately predicted by the QNSE theory.