Local-flux vectors of conserved quantities in the wavenumber space are proposed to investigate their directional properties in anisotropic turbulence. The proposed vectors are validated in statistically steady states of Charney-Hasegawa-Mima turbulence, which consists of anisotropic wave turbulence with zonal flow and isotropic vortex turbulence. The directions of the local-flux vectors are consistent with the energy-enstrophy double cascade in two-dimensional isotropic turbulence. The flux vectors of energy, furthermore, successfully show an anisotropic structure below the Rhines wavenumber, corresponding to the large-scale zonal flow, while those of enstrophy show almost isotropic structure. A couple of expressions of the critical balance are compared with the energy spectra and the flux vectors. The results confirm that the proposed method can quantitatively characterize the anisotropically directed flows of conserved quantities in the wavenumber space.

• Received 25 May 2021
• Accepted 7 December 2021

DOI:https://doi.org/10.1103/PhysRevFluids.7.L012601