Three-wave resonant interactions in two-dimensional turbulence on a rotating sphere
Abstract
Rossby waves are indispensable to discuss flow dynamics under differential rotation, and in particular, three-wave resonant nonlinear interactions of Rossby waves are often considered to play an important roles in realizing characteristic features in Rossby wave turbulences. In fact, at high rotation rates, it has been mathematically shown that the dynamics of two-dimensional Rossby wave turbulence on a beta plane within certain finite time is totally governed by three-wave resonant nonlinear interactions of Rossby waves (Yamada and Yoneda, Physica D, 2013). Also, for example, Kartashova and L’vov (Phys. Rev. Lett., 2007) considered clusters of resonant Rossby waves, defined by connected triangles by nonzero energy transfer, and discussed dynamics of atmosphere. However, what kind of roles the three-wave resonant nonlinear interactions of Rossby waves possess and how they function in two-dimensional turbulences are not at all clear yet, since resonant and non-resonant interactions are always mixed and determine the flow dynamics together in systems having moderate rotation rates, and it is extremely difficult to numerically extract the effect of there-wave resonant interactions there. Therefore in this research, based on the result of Yamada and Yoneda (Physica D, 2013), we have considered two-dimensional Navier-Stokes flows on rapidly rotating spheres, in order to numerically investigate how the three-wave resonant nonlinear interactions of Rossby waves are working in the system. Then it was found that large-scale structures, i.e. zonal flows, cannot be formed only by three-wave resonant interactions. It was also found that, the existence of resonant Rossby waves having no net energy transfer by resonant interactions should not be neglected in considering the dynamics of total resonant Rossby waves dynamics, and as a result, the group of resonant Rossby waves cannot be divided into clusters in terms of connected triangles by nonzero energy transfer.
- Publication:
-
AAS/Division for Planetary Sciences Meeting Abstracts #49
- Pub Date:
- October 2017
- Bibcode:
- 2017DPS....4911512O