Asymptotic systems governed by nonlinear resonant interaction and fluid systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13458
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University
• Principal Investigator: Yamada Michio 京都大学, 数理解析研究所, 教授 (90166736)
• Co-Investigator(Kenkyū-buntansha): 竹広 真一 京都大学, 数理解析研究所, 准教授 (30274426)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 流体 / 波 / 回転流体

Outline of Final Research Achievements

In 2-dimensional Navier-Stokes equations on a rotating sphere at high rotation rates, solutions are shown to converge to those of the fluid equations the nonlinear terms of which consist only of resonant nonlinear interactions. This convergence is understood as a result of the cancellation of non-resonant terms due to high-frequency oscillation. Wave modes corresponding to zonal flows make no contribution to energy transfer through the resonant interactions, but contribute to phase change of other modes. Numerical simulation shows that the phase change brings about a significant effect on the energy transfer among the waves modes, and therefore the zonal flows should be taken into account in the resonant interaction to describe the time-development of the system.

Free Research Field

応用数学，流体力学