Project Fact File

Title: Develop effective and complete low-dimensional models of fluid dynamics
Category: maths
Area: modelling fluid dynamics
No. of units: 1 or 2 or 4
Supervisor: Tony Roberts (Staff Profile)
Description:

This project explores the modelling of turbulent flow is based on analysis of the $k$-$epsilon$ and $k$-$omega$ model of turbulence. It will lead to completely new models for the turbulent dynamics of rivers, estuaries, floods and tsunamis. The new models are designed to explicitly resolve the level of turbulence in the flow and its dynamic interaction with long-wave propagation. Much of the methodology is developed using the example of the dynamics of thin films of fluid. We have shown that cross-stream averaging can lead to error in the derived model. Thus the principle of cross-sectional averaging or depth integration, much used in engineering practise, is valid only in rather special circumstances. Further work on thin fluid films involves modelling flow on generally curved substrates, numerical simulations, and the derivation of initial conditions for the models.

Student: Dian Georgiev, but we need many more for exciting work.