3 years ago

When will the spectral transfers of the two-dimensional passive scalar presenting kinetic energy-enstrophy duality, predicted by the pathological-appearing helical absolute equilibrium, become physically relevant?.

Jian-Zhou Zhu

We offer four arguments to collectively support the conjecture of the possible non-universal genuine transfer directions of two-dimensional (2D) passive scalar energy:

1) The inverse transfer of the magnetic potential energy, in two-dimensional magnetohydrodynamic turbulence, already suggests possibly similar behavior of the corresponding passive scalar, at least when advected by the same/similar velocity and pumped by the similarly correlated (to the active/passive scalar) forcing. 2) The passive cross correlation results in a large-scale concentration of passive-scalar energy in the absolute equilibrium state, with also equipartition at large wavenumbers. 3) Recent numerical data of \textit{rotating flows} with moderate Rossby number showing inverse transfers of the vertically-averaged vertical velocity, could be related. 4) The preliminary calculations of a modification of the Kraichnan passive scalar model indicates that some details of the passive scalar pumping, taken here passively correlated to/dependent on the vorticity, indeed matter.

The conjecture is highly speculative, and so far there is no solid argument proving or disproving it. The absolute equilibrium spectra in the above item 2) present pathology in the sense that the 2D horizontal flow spectrum being affected by the passive scalar, which is a problem in the mathematics or logic that statistical correlation does not reflect the dynamical mechanism of passive or active correlation. Such a pathology can be cured in situations when the 2D3C dynamics are dominant but with some partial coupling perturbation; and, a flow uniformly with the real Schur form of the velocity gradient in a fixed Cartesian coordinate frame appears to be a good model for such a repairing mechanism.

Publisher URL: http://arxiv.org/abs/1408.1503

DOI: arXiv:1408.1503v4

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