Postdoctoral Research Associate position is open
for a fixed one-year term to commence work in 2007.
The appointment is expected to be made at Academic Level A with the salary $56,419 p.a.The position is funded from the Australian Research Council grant for the project Systematically model the large-scale complexity of turbulent floods and thin film flows.
The project
This project aims to continue to develop and use systematic analytical techniques for the construction of relatively simple models of turbulent floods and other related fluid dynamics. Its parallel goals are: to produce mathematical methods of analysis of wide ranging applicability in the modelling of dynamics; and to make specific applications of the innovative analytical and numerical techniques to important problems in fluid dynamics in order to extend our basic understanding of and ability to simulate large-scale turbulent flows and thin layers of fluid.More details are available at http://www.sci.usq.edu.au/research/TAM/restud.html.
The position
Successful candidate will be selected according to the following criteria:- PhD, or equivalent, in a relevant area with a commitment to high quality research;
- expertise in fluid mechanics, particularly free-surface hydrodynamics, and dissipative systems; knowledge of centre manifolds and/or computer algebra is desirable;
- communication skills;
- energy and initiative.
Method of application
will be announced soon. For more details contact Dr. Dmitry Strunin (strunin@usq.edu.au) or Prof. Tony Roberts (aroberts@usq.edu.au).Department of Mathematics and Computing
forms a vital part of a developing regional university and offers courses in Applied Mathematics, Statistics and Computer Science. It has a large base of networked computers, supports conference participation, and accesses libraries around Australia. Further information about the department, its research and courses is obtainable from http://www.sci.usq.edu.au.Background and aims of the project
Following previously funded development of modelling the flow of thin fluid layers, this project aims to continue to develop and use systematic analytical and numerical techniques for the construction of relatively simple but accurate dynamical models of the turbulent flow of relative shallow fluid as occur in floods and in breaking waves on the shore. These models will be developed with comparison to established observations and laboratory experiments on turbulent flow. The innovative modelling of a laminar flow of a thin layer of fluid will also be extended as a test bed for developing numerical and analytical techniques.
In fluid dynamics, when the geometry indicates that the dynamics in one or more spatial dimensions are in some sense subservient to the others, then we seek models describing the dynamics in just the interesting spatial dimensions. Examples are the turbulent flow of shallow water in an estuary or flood \cite[e.g.]{Shiono91, Stansby97, Mei94, Roberts99c}, the dispersion of pollutant in a river or pipe \cite[e.g.]{Balakotaiah92, Chatwin85, Chikwendu86a, Mercer94a, Rosencrans93, Taylor53, Smith01} and the flow of a thin film of fluid over a solid surface \cite[e.g.]{Chang94, Prokopiou91b, Quere99} and its transport of material \cite[e.g.]{Halpern92b, Jensen93, Dewitt94}. The enormous level of detail in a full physical description of a large scale system makes the flow impossible to simulate in full detail, and thus tractable simple approximations have been derived over many years. For example, turbulent floods have typically been described by the local water depth and the local mean fluid velocity. Such approximations have traditionally been obtained by averaging over the cross-flow structures \cite[e.g.]{Fredsoe92, Rastogi78, Keller88}; but remarkably such averaging is unsound as a modelling paradigm \cite[p153]{Kuznetsov95}. However, the development of centre manifold theory \cite[e.g.]{Gallay93, Haragus95} and associated techniques \cite{Roberts88a, Roberts94c} may put these simpler dynamical models on a firm basis and thereby create new and quantitatively accurate analytic and numerical models. We will continue to do precisely this for large horizontal scale turbulent flows with a free surface, and benchmark the resulting models to extant and new laboratory experiments.
The key theoretical tool is that of centre manifolds \cite[e.g.]{Carr81}, a powerful and widely applicable theory that is used rationally to derive and extend many of the heuristic models of mechanics \cite[e.g.]{Armbruster89, Balakotaiah92, Boe89, Chang89, Chossat85, Hwang89, Meron8 6b, Newell93, Renardy89}. The theory eliminates consistently many of the unnecessary physical ``modes'' of a system, and deals instead with a lower-dimensional system with equivalent long-term dynamical behaviour. Other mathematical methods do this to some extent, for example the method of multiple scales \cite[e.g.]{Oron97}, the slaving principle of synergetics \cite{Haken83}, the renormalisation group method \cite[e.g.]{Ei99}, methods for perturbed Hamiltonian systems \cite{Groesen89}, or inertial manifolds \cite{Temam90}. However, none are so clear nor so generally applicable as the dynamical system techniques which we have developed, and none supply the additional initial and boundary conditions which are essential for a complete model. The methodology in the modelling stage resolves physical microscale dynamics and interactions to derive a description of the dynamics of the macroscopic variables of interest.
Our research group uniquely has the expertise to build this bridge between dynamical complex systems theory and practical fluid modelling applications.