On a quasi-invariant associated with the emergence of anisotropy in two-dimensional turbulence on a rotating sphere

To provide a theoretical explanation for the emergence of zonally elongated structures from two-dimensional turbulence on a rotating sphere,a quasi-invariant of the system is obtained by a minimization process,which is a straightforward extension of a similar process proposed by a previous study on β-plane turbulence to the spherical geometry. the quasi-invariant is defined as a weighted sum of the energy density in the wavenumber space. the distribution of the weighting coefficient has airfoil-shaped contours,with which the anisotropic energy transfer that favors zonally elongated structures can be explained. large number of numerical time-integrations of decaying two-dimensional turbulence on a rotating sphere are conducted to examine the conservation of the quasi-invariant. it is shown that the quasi-invariant is conserved well when the nonlinearity of the system is sufficiently weak; furthermore,energy is transferred in the wavenumber space apparently along the airfoil-shaped contours of the weighting coefficient for the quasi-invariant. © 2016,meteorological society of japan.