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Doctoral Thesis
Full name
André Seiji Wakate Teruya
Knowledge Area
Date of Defense
São Paulo, 2019
Raupp, Carlos Frederico Mendonça (President)
Barros, Saulo Rabello Maciel de
Dias, Pedro Leite da Silva
Gutierrez, Enver Manuel Amador Ramirez
Peixoto, Pedro da Silva
Title in English
Nonlinear Interaction of Gravity and Acoustic Waves
Keywords in English
acoustic waves
gravity waves
nonhydrostatic atmospheric model
nonlinear interactions
normal modes
Abstract in English
Here we have investigated the possibility of an inertio-acoustic wave-mode to be unstable with regard to gravity mode perturbations through nonlinear triad interactions in the context of a shallow nonhydrostatic model. We have considered highly truncated Galerkin expansions of the perturbations around a resting, hydrostatic and isothermal background state in terms of the eigensolutions of the linear problem. For a single interacting wave triplet, we have shown that an acoustic mode cannot amplify a pair of inertio-gravity perturbations due to the high mismatch among the eigenfrequencies of the three interacting wave-modes, which resquires an unrealistically high amplitude of the acoustic mode in order for pump wave instability to occur. In contrast, it has been demonstrated by analyzing the dynamics of two triads coupled by a single mode that a non-hydrostatic gravity wave-mode participating of a nearly resonant interaction with two acoustic modes can be unstable to small amplitude perturbations associated with a pair of two hydrostatically balanced inertio-gravity wave-modes. This linear instability yields significant inter-triad energy exchanges if the nonlinearity associated with the second triplet containing the two hydrostatically balanced inertio-gravity modes is restored. Therefore, this inter-triad energy exchanges lead the acoustic modes to yield significant energy modulations in hydrostatic inertio-gravity wave modes. The implications of the results for the nonlinear hydrostatic adjustment problem are discussed.
Title in Portuguese
Intera c oes N ao-Lineares entre Ondas de Gravidade e Ac usticas
Keywords in Portuguese
interações não-lineares
modelos não-hidrostáticos.
modos normais
ondas acústicas
ondas de gravidade
Abstract in Portuguese
Neste trabalho investigou-se a possibilidade de ondas ac usticas serem inst aveis em rela c ao `a perturba c oes nos modos gravidade-inerciais, atrav es de intera c oes tri adicas n ao- lineares no contexto do modelos n ao-hidrosat atico raso. Foi considerado uma expans ao de Galerkin, altamente truncada, das perturba c oes em torno de um campo b asico isot ermico, hidrost atico e em repouso. A expans ao de Galerkin foi feita em rela c ao `as autofun c oes do problema linearizado. Para um tripleto isolado, ficou demonstrado que uma onda ac ustica n ao consegue amplificar as perturba c oes de um par de ondas gravidade-inerciais. Isso ocorre devido ao alto mismatch das autofrequencias do tripleto de ondas. Por outro lado, a an alise da dinamica de dois tripletos acoplados por um unico modo demonstrou que um modo gravidade-inercial n ao-hidrost atico (ac ustico), participando de um tripleto quase- ressonate com dois modos ac usticos (um modo gravidade-inercial e um modo ac ustico) pode ser inst avel em rela c ao `a pequenas perturba c oes associadas a um par de ondas gravidade- inerciais que est ao em balan co hidrost atico. Esta instabilidade linear implica em uma troca de energia inter-tri adica significativa, se a n ao-linearidade associada ao segundo tri- pleto, composto por dois modos gravidade-inearciais hidrost aticos, for reconsiderada. As implica c oes desses resultados para o ajuste hidrost atico n ao-linear s ao discutidas.
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