Energetics of Glocal Nonhydrostatic Normal Modes

Author(s)

André Seiji Wakate Teruya

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto Astronômico e Geofísico (IAG/SBD)
• Defense date: 2014-04-23

Examining board members

Carlos Frederico Mendonça Raupp; Jose Paulo Bonatti; Pedro Leite da Silva Dias

• Advisor: Carlos Frederico Mendonça Raupp

Abstract

In the present monograph the linear and weakly nonlinear energetics of the normal modes of a nonhydrostatic, compressible, and baroclinic global atmospheric model was analized. The normal modes are the linear free wave solutions of a dynamical system linearized around a basic state that is hydrostatic and at rest. Nevertheless, it was assumed an isothermal basic state, so the mathematical treatment of the problem becomes less cumbersome. The eigenfunctions of this set of linearized equations are obtained by the method proposed by \\cite{kasahara2000}. Then the total energy associated with the perturbations and its components are derived from the governing equations in their Eulerian representation. Next, the functional relation between these energies and the zonal wavenumber of the inertia-gravity and acoustic-inertia modes is analyzed. From the normal mode\'s energetics it is shown that the nonhydrostatic effects are more apparent on the shorter inertia-gravity modes. It is also shown that the vertical kinetic energy and the elastic energy of the acoustic-inertia modes are the dominant kind of energy of these modes. Although as the zonal wavenumber becomes bigger, the importance of the elastic energy grows and the vertical kinetic energy becomes less significant. (AU)

• FAPESP's process: 12/06388-8 - Energetics of the Normal Modes of the Nonhydrostatic Atmospheric Dynamics
• Grantee: André Seiji Wakate Teruya
• Support Opportunities: Scholarships in Brazil - Master