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Zonal flows and wave resonance. --- Rossby wave case ---

Presented by: 
Michio Yamada Kyoto University
Wednesday 9th August 2017 - 16:00 to 17:00
INI Seminar Room 1
We discuss resonant and nonresonant interaction of waves and time-development of energy distribution in a wave system.   We take, not a water wave system, but a Rossby wave system on a rotating sphere, where spherical harmonic functions correspond to Rossby waves which are labelled by total wave number and longitudinal wavenumber.    In the Rossby wave system, a zonal flow pattern is known to emerge even from random and isotropic initial conditions in the course of time development.  We classify the Rossy waves into 4 groups according to whether it has resonant waves or  not, and also whether  it represents a zonal flow (i.e. with zero longitudinal wavenumber) or not.  Numerical simulation shows that when there is no zonal energy initially, the energy goes into zonal resonant modes from nonzonal and nonresonant modes, which suggests that the nonresonant interaction between the nonzonal nonresonant modes and the zonal resonant modes plays a dominant role in the formation of the zonal flows.  Introducing 'effective energy transfer',  which enables us to talk about the energy transfer from one mode to another mode,  we find that the nonresonant interaction transfers energy from the nonresonant mode mostly to the resonant modes.  
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons