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SUMMARY:Formation of large-scale zonal flows in two-dimensional turbulence
  on a rotating sphere - Kiori Obuse (Okayama University)
DTSTART:20240116T100000Z
DTEND:20240116T104500Z
UID:TALK208465@talks.cam.ac.uk
DESCRIPTION:Two-dimensional barotropic flow on a rotating sphere is one of
  the simplest mathematical models describing the dynamics of planetary atm
 ospheres. This model is very simple and does not take into account three-d
 imensional 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 mo
 del also has the interesting aspect that it has the same mathematical stru
 cture as the special case of Hasegawa-Mima equation when a plane approxima
 tion is applied to it.\nIn this talk\, we consider unforced two-dimensiona
 l turbulence on a rotating sphere and discuss how the nonlinear interactio
 ns of Rossby waves\, which are linear wave solutions unique to rotating sy
 stems\, are involved in the formation of the large-scale zonal flows (west
 ward 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 int
 eraction of Rossby wave strongly dominates the dynamics of the flow field 
 [5\,6]. However\, it is not possible to transfer energy to Rossby waves co
 rresponding to zonal flows (zonal Rossby waves) directly by three-wave res
 onance interactions [7\,8]. This means that the formation of zonal flows t
 akes 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 in
 capable of non-resonant interactions. [8].\nBased on our recent detailed n
 umerical calculations of energy transfer by Rossby wave three-wave non-res
 onant interactions\, we report that the formation of the westward circumpo
 lar flow is due to non-local energy transfer by three-wave near-resonant i
 nteractions (special cases of non-resonant interactions).\n&nbsp\;\nRefere
 nces\n[1] S. Yoden and M. Yamada\, J. Atomos. Sci. 50\, 631 (1993)\n[2] S.
  Takehiro et al.\, J. Atmos. Sci. 64\, 4084 (2007)\n[3] T. Nozawa and S. Y
 oden\, Phys. Fluids 9\, 2081 (1997)\n[4] K. Obuse et al.\, Phys. Fluids. 2
 2\, 056601 (2010)\n[5] M. Yamada and T. Yoneda\, Physica D 245\, 1 (2013)\
 n[6] A. Dutrifoy and M. Yamada\, In preparation.\n[7] G. M. Reznik et al.\
 , Dyn. Atmos. Oceans 18\, 235 (1993).\n[8] K. Obuse and M. Yamada\, Phys. 
 Rev. Fluids 4\, 024601 (2019)\n&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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