Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

TL;DR

This paper analyzes the anisotropic energy distribution of internal gravity waves in strongly stratified turbulence, proposing new indices and methods to better understand the wave-eddy interactions and energy spectra.

Contribution

It introduces novel anisotropic spectral analysis techniques and indices to distinguish wave-dominated regimes in stratified turbulence, addressing limitations of isotropic analyses.

Findings

Identification of anisotropic energy distribution in wave-number space.

Verification of wave dominance through frequency deviation analysis.

Determination of critical wave number based on anisotropic time scales.

Abstract

Stratified turbulence shows scale- and direction-dependent anisotropy and the coexistence of weak turbulence of internal gravity waves and strong turbulence of eddies. Straightforward application of standard analyses developed in isotropic turbulence sometimes masks important aspects of the anisotropic turbulence. To capture detailed structures of the energy distribution in the wave-number space, it is indispensable to examine the energy distribution with non-integrated spectra by fixing the codimensional wave-number component or in the two-dimensional domain spanned by both the horizontal and vertical wave numbers. Indices which separate the range of the anisotropic weak-wave turbulence in the wave-number space are proposed based on the decomposed energies. In addition, the dominance of the waves in the range is also verified by the small frequency deviation from the linear dispersion relation. In the wave-dominant range, the linear wave periods given by the linear dispersion relation are smaller than approximately one third of the eddy-turnover time. The linear wave periods reflect the anisotropy of the system, while the isotropic Brunt-V\"ais\"al\"a period is used to evaluate the Ozmidov wave number, which is necessarily isotropic. It is found that the time scales in consideration of the anisotropy of the flow field must be appropriately selected to obtain the critical wave number separating the weak-wave turbulence.