Energetics of the normal modes of the Nonhydrostatic atmospheric dynamics

• Grant number: 12/06388-8
• Support type: Scholarships in Brazil - Master
• Effective date (Start): June 01, 2012
• Effective date (End): February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Geosciences
• Principal Investigator: Carlos Frederico Mendonça Raupp
• Grantee: André Seiji Wakate Teruya
• Home Institution: Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 09/11643-4 - Multi-scale interactions in the atmosphere, AP.JP

Abstract

The goal of this research project is to analyze the energetics of the normal modes of a global, compressible, baroclinic and non-hydrostatic atmospheric model in spherical coordinates. These normal modes correspond to the eigensolutions of the governing equations of the present model, linearized around a basic state at rest and satisfying the hydrostatic balance. Furthermore, to simplify the analysis somewhat, we will consider in the present work an isothermal basic state. In this way, the model equations to be analyzed here refer to the linearized version of the momentum, thermodynamics for dry adiabatic motions and the continuity equations, considering a resting, hydrostatic and isothermal background state. The first step of this project has already been done in the Scientific Initiation project of the student, which consists of the computing implementation of the calculus of the eigenfrequencies and equivalent heights of the normal modes, following the methodology described in Kasahara and Qian (2000). Thus, the present project is a follow up work of the Scientific Initiation program, where we plan to derive from the governing equations for the perturbations the total energy of the model and, by using the Parseval's identity, we aim to compute the model decomposition of the total energy and to analyze how the different forms of this energy varies with the zonal wavenumber, meridional mode and vertical mode, for all the possible mode types. We expect that this work will provide a better understanding on the hydrostatic adjustment processes in the atmosphere, as well as an important contribution for the project "Multi-Scale Interactions in the Atmosphere" (FAPESP Process number 2009/11643-4).

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

RAUPP, CARLOS F. M.; TERUYA, ANDRE S. W.; SILVA DIAS, PEDRO L. Linear and Weakly Nonlinear Energetics of Global Nonhydrostatic Normal Modes. JOURNAL OF THE ATMOSPHERIC SCIENCES, v. 76, n. 12, p. 3831-3846, DEC 2019. Web of Science Citations: 1.