Nonconservative and reverse spectral transfer in Hasegawa--Mima turbulence
Nonconservative and reverse spectral transfer in Hasegawa--Mima turbulence The dual cascade is generally represented as a conservative cascade of enstrophy to short wavelengths through an enstrophy similarity range and an inverse cascade of energy to long wavelengths through an energy similarity range. This picture, based on a proof due to Kraichnan [Phys. Fluids [bold 10], 1417 (1967)], is found to be significantly modified for spectra of finite extent. Dimensional arguments and direct measurement of spectral flow in Hasegawa--Mima turbulence indicate that for both the energy and enstrophy cascades, transfer of the conserved quantity is accompanied by a nonconservative transfer of the other quantity. The decrease of a given invariant (energy or enstrophy) in the nonconservative transfer in one similarity range is balanced by the increase of that quantity in the other similarity range, thus maintaining net invariance. The increase or decrease of a given invariant quantity in one similarity range depends on the injection scale and is consistent with that quantity being carried in a self-similar transfer of the other invariant quantity. This leads, in an inertial range of finite size, to some energy being carried to small scales and some enstrophy being carried to large scales.
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