Mathematical and computational modeling of nonlinear waves in inviscid fluids

SIN RESUMEN

This proposal is structured around two thematic axes: 1. Study of water waves in channels with variable seabed: Our main goal is to understand the characteristics of waves generated by different types of seabed displacements. Additionally, we aim to obtain a comprehensive view of the underwater velocity field and investigate the particle trajectories resulting from the interaction between surface waves, currents, and submarine relief. This study can be applied to the investigation of seismic events that lead to tsunami formation and the definition of safety criteria for underwater operations. More specifically, the first thematic axe can be divided into two directions: (i) waves generated by variations in the seabed in both space and time simultaneously, which can be physically interpreted as the generation of waves caused by seismic events; (ii) waves propagating in channels with seabeds that vary only in space. From a scientific perspective, direction (i) offers the potential for significant contributions, particularly through the enhancement of the time-dependent conformal mapping developed by Poletto et al. 2017. This will enable more comprehensive computational simulations of seabed geometric configurations than those currently available in the literature. Furthermore, our research will provide a nonlinear analysis of surface waves, contrasting with the predominantly linear dynamics employed so far. As for direction (ii), we intend to investigate the formation of a streamline pattern known as “Kelvin cat eyes,” which occurs in flows with constant vorticity. This phenomenon has only been studied for linear waves in Flamarion et. al 2020 and in Nachbin and Ribeiro-Jr 2017, and in this project, we aim to expand this analysis to nonlinear waves. 2. Study of waves in flows coupled with an electric field: We aim to understand how variations in the electric field can influence the trajectories of fluid particles, as well as investigate the dynamics of waves in electrohydrodynamic flows in channels with variable bottoms. The main scientific contribution will be to expand the current understanding of how fluid motion can be modified by adjusting the intensity of the electric field. This question is of great relevance in industry, for example, in electrostatic liquid film radiators (Griffing et al. 2006), cooling systems in conductive pumps (Ghoshal and Miner 2003), and lithography-induced self-organization using liquid films in microfluidic scales (Wu and Russel 2006).

Thematic Axis 1: Study of Water Waves in Channels with Variable Submarine Topography OE1: Develop fast and robust numerical schemes to simulate the generation of nonlinear waves resulting from different types of seabed crust displacements, considering the context of the full Euler equations. OE2: Investigate the formation of the streamline pattern known as "Kelvin cat eyes" in flows with constant vorticity and variable topography. Thematic Axis 2: Study of Waves in Flows Coupled with an Electric Field OE3: Investigate the effect of horizontal and normal electric fields on the fluid body in two-dimensional electrodynamic flows in channels occupied by a dielectric fluid and a conducting gas. OE4: Obtain insights into the velocity field within the fluid body in electrodynamic flows in channels occupied by two immiscible fluids with different densities. OE5: Develop fast and robust numerical methods to compute the velocity field and pressure within the fluid body in the scenarios described above.

Investigacion basica

Interdisciplinario

CONCURSO ANUAL DE INVESTIGACIÓN

• 74 — Matemáticas aplicadas

Ciencias naturales - Matemáticas - Matemáticas aplicadas

PONTIFICIA UNIVERSIDAD CATÓLICA DEL PERÚ