Variational multiscale models of turbulent environmental flows (DCB.6283)

This proposal considers the development of variational multiscale techniques for turbulent flows, such as in rivers, lakes, lagoons and harbours. An understanding of turbulent flows and the ability to simulate them is crucial as they occur everywhere in nature. Turbulence promotes mixing, chemical reactions and influences transport within a flow. These effects are important for the prediction of contaminant transport, sediment transport, erosion and deposition. Turbulent flows are characterised by an extreme range in the scales of motion. This makes the direct numerical simulation of turbulent flows extremely difficult. Even with the most powerful computers, it is not possible to resolve all scales of motion for practical flows.
The variational multiscale approach relies on splitting the velocity field of a turbulent flow into different scales, depending on how rapidly they vary in space or time. Casting the problem in a variational framework yields an equation for each scale of motion. In the proposed work, the fine-scale equations are solved approximately, and their influence is included in the coarse scales of motion, which are solved using a numerical method. A key aspect is how the small-scale equation is approximated. An approximate solution of the fine-scale equation will lead to subgrid scale models that depart from the traditional eddy-viscosity concept. In particular, the approach will be applied for shallow water flows, with an emphasis on modelling mixing and transport phenomena.
By examining the equations that govern fluid flow in an innovative format, new insights will be gained, leading to new models for turbulent flows. The new models will allow the numerical simulation of important problems such as transport or sediment and scouring in a harbour due to turbulence, or the mixing of pollutants in a lake. The methodology can be extended to other fields of mechanics where multiscale phenomena are important.

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