Sloshing of shallow water on a bounded domain
Lead Research Organisation:
University of Surrey
Department Name: Mathematics
Abstract
This project is a study of linear and nonlinear hyperbolic partial differential equations, combining both theory and applications.
After looking at sloshing of shallow water in a vessel for the first part of the project we now consider more general hyperbolic systems. We aim to analyse the stability of such systems using a geometric optics expansion method. This will begin with looking at symmetric hyperbolic systems with the goal of applying what is learned there to equations with different properties. This will tie in with the previous research on the shallow water sloshing as that is an example of the type of system that this method can be applied to. The main aim being to develop rigorous theory regarding equations of hyperbolic type. Applications of the research include any physical problem where the underlying equations that describe the fluid flow are of hyperbolic type, e.g. sloshing of water or gas in a container.
After looking at sloshing of shallow water in a vessel for the first part of the project we now consider more general hyperbolic systems. We aim to analyse the stability of such systems using a geometric optics expansion method. This will begin with looking at symmetric hyperbolic systems with the goal of applying what is learned there to equations with different properties. This will tie in with the previous research on the shallow water sloshing as that is an example of the type of system that this method can be applied to. The main aim being to develop rigorous theory regarding equations of hyperbolic type. Applications of the research include any physical problem where the underlying equations that describe the fluid flow are of hyperbolic type, e.g. sloshing of water or gas in a container.
Organisations
People |
ORCID iD |
| Thomas Bridges (Primary Supervisor) | |
| Nicholas Burgess (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509772/1 | 01/10/2016 | 30/09/2021 | |||
| 1942698 | Studentship | EP/N509772/1 | 01/10/2017 | 31/03/2021 | Nicholas Burgess |
| Description | The focus of the work has been shifted to studying symmetric Hamiltonion systems. The previous work on sloshing became a much harder analytical problem than first anticipated. The new topic has been very rewarding as I am able to fully understand the modulation of these systems in the ODE and PDE cases. We also look at relative perioidic orbits, which in the ODE case are fully understood. Another part of the work has been using results on modulating in a characteristic frame, and applying this to other problems including in a pattern formation setting. |
| Exploitation Route | The work, although still ongoing, could impact the mathematical nonlinear waves community with others within this field working on similar problems or applying what is learned here in other contexts. |
| Sectors | Other |