Hamiltonian methods in fluids and plasmas

• Grant number: 25/03868-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Breno Raphaldini Ferreira da Silva
• Grantee: Adhara Batista Guimarães Carvalho
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/16513-9 - Nonlinear dynamics, wave interactions and coherent structures in atmospheric and solar flows, AP.JP

Abstract

Waves, such as Rossby and inertial-gravity waves, constitute one of the fundamental mechanisms of geophysical fluid dynamics, and are essential for understanding the dynamics of the atmosphere and oceans. Tools originating in classical mechanics, such as Lagrangian and Hamiltonian methods, provide an elegant approach to the study of waves in geophysical fluids, highlighting the role of the link between symmetries and conservation laws of the system. In the present project, we intend to explore such methods in the context of atmospheric and oceanic wave propagation. Starting from a basic model of the shallow water equations, we will explore topics such as wave dispersion, propagation in inhomogeneous media, wave breaking, conservation of wave activity and nonlinear wave interactions. The theoretical study of these topics will be complemented with numerical solutions in simplified situations.