Energy Transfer to Resonant Zonal Rossby Modes in Two-Dimensional Turbulence on a Rotating Sphere

Abstract

The transfer of energy by the nonlinear interaction of Rossby waves in two-dimensional turbulence on a rotating sphere was investigated in this study. Although it has been suggested that three-wave resonant interaction dominates nonlinear interactions when the rotation rate of the sphere is sufficiently high, resonant interactions do not transfer energy to zonal Rossby waves, resulting in the nonresonant interaction of Rossby waves being responsible for the generation of zonal flows [Reznik, Piterbarg, and Kartashova, Dyn. Atmos. Oceans 18, 235 (1993); Obuse and Yamada, Phys. Rev. Fluids 4, 024601 (2019)]. The resonant and nonresonant interactions of Rossby waves were investigated in this study, and it was found that although energy is transferred to the zonal Rossby modes by the nonresonant three-wave interaction of Rossby waves, the target of this nonresonant energy transfer is only the resonant zonal Rossby waves.