Local energy-flux vectors and nonlocal resonant interactions in stratified turbulence
Energy flux in the wavenumber space plays a crucial role in the cascade theory of turbulence. In anisotropic turbulence such as stratified turbulence, the energy flux is evaluated as anisotropic and directional vectors, and is expected to be drawn as the paths of the energy transfer from the external input to the dissipation. Such local energy-flux vectors can be uniquely determined by introducing two ansatzes, the net locality and the efficiency of the energy transfer. On the other hand, the weak turbulence theory indicates that nonlocal resonant interactions called induced diffusion are dominant in the energy transfer of internal-wave turbulence in the anisotropic and scale-invariant limit. Interestingly, the "local’’ energy-flux vectors numerically obtained from a direct numerical simulation are consistent with the energy transfers due to the "nonlocal’’ resonant interactions. This paradoxical contradiction of the locality will be discussed.
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