Graphical Abstract

Saito, I., and K. Ishioka, 2016: On a quasi-invariant associated with the emergence of anisotropy in two-dimensional turbulence on a rotating sphere. J. Meteor. Soc. Japan, 94, 25-39.
https://doi.org/10.2151/jmsj.2016-002 Graphical Abstract with highlights

A quasi-invariant for the vorticity equation on a rotating sphere is obtained by a minimization process.
The distribution of the weighting coefficient for the quasi-invariant has airfoil-shaped contours (Fig. 1, solid curves), with which the anisotropic energy transfer that favors zonally elongated structures can be explained.
Freely-evolving turbulence experiments confirm that the quasi-invariant is conserved well when the nonlinearity of the system is sufficiently weak.
When the quasi-invariant is conserved well, energy is transferred in the wavenumber space apparently along the airfoil-shaped contours of the weighting coefficient for the quasi-invariant (Fig. 1).