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

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