# Analyzing Oceanic Turbulence Using Structure Functions and Advanced Turbulence Theories via Satellite Altimetry

**Event: **2018 Ocean Surface Topography Science Team Meeting

**Session: **Others (poster only)

**Presentation type: **Type Poster

Along-track records provide a powerful tool for extracting spectral characteristics of turbulence using physical space measurements. Combined with advanced theories of turbulence, these tools can be used for various analyses of ocean mixing on various spatial and temporal scales.

A quasi-normal scale elimination (QNSE) turbulence theory has been developed for neutrally stratified rotating flows. The theory provides near-first principle framework for the representation of turbulence anisotropization under the action of rotation. The anisotropization results in the emergence of different eddy viscosities and eddy diffusivities in different directions and directional dependence of the kinetic and potential energies spectra. There is also a little known phenomenon of componentality, i.e., the emergence of eddy viscosities that are different for different velocity components.

The Woods scale that involves the viscous dissipation rate characterizes the crossover between the turbulence and inertial wave domains and is analogous to the Ozmidov scale in flows with stable stratification.

Rapid rotation renders the horizontal eddy viscosity negative, and so the derivations are carried out in a weak rotation limit. Within that limit, an analytical theory of the transition from the Kolmogorov to a rotation-dominated turbulence regime is developed. The dispersion relation of linear inertial waves is unaffected by turbulence while all one-dimensional energy spectra undergo steepening from the Kolmogorov -5/3 to the -3 slope. The analytically derived longitudinal and transverse spectra are congruent to the atmospheric spectra by Nastrom & Gage, both qualitatively and quantitatively. Thus, for the first time, these spectra are obtained fully analytically. QNSE explains the latitudinal dependence of the spectra and lends itself for practical applications in simulations of atmospheric and oceanic flows as it produces closed expressions for the eddy viscosities and eddy diffusivities. The analytical expressions for the spectra can be used to derive expressions for the second order structure functions that are in good agreement with data and estimates by Lindborg (1999). QNSE theory reveals that on synoptic scales, the dynamics, the spectra and the structure functions are determined not by flow two-dimensionalization and ensuing direct enstrophy cascade but by suppression of flow dimensionality by rotation. The ratio of the analytically derived transverse and longitudinal second-order structure functions corresponds to a spatial dimension of the system to be lesser than 3 but larger than 2.

By exhibiting dependence on the Coriolis parameter only, these results apply to oceanic flows as well as the atmospheric flows. The new physics revealed by the QNSE theory requires re-evaluation of some basic ideas at the foundation of our understanding of geophysical turbulence in general and ocean mixing in particular.

A quasi-normal scale elimination (QNSE) turbulence theory has been developed for neutrally stratified rotating flows. The theory provides near-first principle framework for the representation of turbulence anisotropization under the action of rotation. The anisotropization results in the emergence of different eddy viscosities and eddy diffusivities in different directions and directional dependence of the kinetic and potential energies spectra. There is also a little known phenomenon of componentality, i.e., the emergence of eddy viscosities that are different for different velocity components.

The Woods scale that involves the viscous dissipation rate characterizes the crossover between the turbulence and inertial wave domains and is analogous to the Ozmidov scale in flows with stable stratification.

Rapid rotation renders the horizontal eddy viscosity negative, and so the derivations are carried out in a weak rotation limit. Within that limit, an analytical theory of the transition from the Kolmogorov to a rotation-dominated turbulence regime is developed. The dispersion relation of linear inertial waves is unaffected by turbulence while all one-dimensional energy spectra undergo steepening from the Kolmogorov -5/3 to the -3 slope. The analytically derived longitudinal and transverse spectra are congruent to the atmospheric spectra by Nastrom & Gage, both qualitatively and quantitatively. Thus, for the first time, these spectra are obtained fully analytically. QNSE explains the latitudinal dependence of the spectra and lends itself for practical applications in simulations of atmospheric and oceanic flows as it produces closed expressions for the eddy viscosities and eddy diffusivities. The analytical expressions for the spectra can be used to derive expressions for the second order structure functions that are in good agreement with data and estimates by Lindborg (1999). QNSE theory reveals that on synoptic scales, the dynamics, the spectra and the structure functions are determined not by flow two-dimensionalization and ensuing direct enstrophy cascade but by suppression of flow dimensionality by rotation. The ratio of the analytically derived transverse and longitudinal second-order structure functions corresponds to a spatial dimension of the system to be lesser than 3 but larger than 2.

By exhibiting dependence on the Coriolis parameter only, these results apply to oceanic flows as well as the atmospheric flows. The new physics revealed by the QNSE theory requires re-evaluation of some basic ideas at the foundation of our understanding of geophysical turbulence in general and ocean mixing in particular.