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Formation of large-scale zonal flows in two-dimensional turbulence on a rotating sphere

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ADIW01 - Layering — A structure formation mechanism in oceans, atmospheres, active fluids and plasmas

Two-dimensional barotropic flow on a rotating sphere is one of the simplest mathematical models describing the dynamics of planetary atmospheres. This model is very simple and does not take into account three-dimensional fluid motion, planetary topography, or, in many cases, heat distribution for example. Nevertheless, it exhibits rich fluid dynamics, including the formation of large-scale zonal flows [1,2,3,4]. This model also has the interesting aspect that it has the same mathematical structure as the special case of Hasegawa-Mima equation when a plane approximation is applied to it. In this talk, we consider unforced two-dimensional turbulence on a rotating sphere and discuss how the nonlinear interactions of Rossby waves, which are linear wave solutions unique to rotating systems, are involved in the formation of the large-scale zonal flows (westward circumpolar flows in this case. ). It is known that when the rotation rate of the sphere is very high, the three-wave resonance non-linear interaction of Rossby wave strongly dominates the dynamics of the flow field [5,6]. However, it is not possible to transfer energy to Rossby waves corresponding to zonal flows (zonal Rossby waves) directly by three-wave resonance interactions [7,8]. This means that the formation of zonal flows takes place by weakly existing non-resonant interactions, but the details have been little understood. In particular, we still do not know why the zonal flows that develop due to non-resonant interactions consist of waves that are capable of resonant interactions, rather than waves that are incapable of non-resonant interactions. [8]. Based on our recent detailed numerical calculations of energy transfer by Rossby wave three-wave non-resonant interactions, we report that the formation of the westward circumpolar flow is due to non-local energy transfer by three-wave near-resonant interactions (special cases of non-resonant interactions).   References [1] S. Yoden and M. Yamada, J. Atomos. Sci. 50, 631 (1993) [2] S. Takehiro et al., J. Atmos. Sci. 64, 4084 (2007) [3] T. Nozawa and S. Yoden, Phys. Fluids 9, 2081 (1997) [4] K. Obuse et al., Phys. Fluids. 22, 056601 (2010) [5] M. Yamada and T. Yoneda, Physica D 245 , 1 (2013) [6] A. Dutrifoy and M. Yamada, In preparation. [7] G. M. Reznik et al., Dyn. Atmos. Oceans 18, 235 (1993). [8] K. Obuse and M. Yamada, Phys. Rev. Fluids 4, 024601 (2019)    

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