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The behaviour of particle pairs in kinematic simulations

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If you have a question about this talk, please contact Mustapha Amrani.

The Nature of High Reynolds Number Turbulence

The way pairs of particles separate is an important aspect of turbulent mixing which has often been explored using the technique of kinematic simulation. However kinematic simulation is not like real turbulnce in that the Fourier modes are independent and the smaller eddies are not advected (or ‘swept’) by the large eddies. Our aim here is to explore this aspect of kinematic simulation both theoretically and numerically.

The fact that the small eddies are not swept by the large eddies, but the particles in the flow are so swept, means that particle pairs are swept through the smaller eddies by the large eddies. This is expected to alter the time scale on which the relative velocity of the particles fluctuates. A simple argument then shows that the mean square separation of pairs is expected to grow, not as t cubed as expected following Richardson, but as t to the sixth power. This is confirmed in numerical simulations where we add a mean flow to the kinematic flow field to exaggerate the problem caused by lack of sweeping (with the eddies not being advected by the mean flow). Without the mean flow the situation is more complex with a significant contribution to the separation process from locations where the velocity is small and where there is no sweeping issue. This leads to a separation growing like t to the power 9/2. The time dependence of the kinematic flow field can also lead to a wider range of behaviours.

The work described here is not especially new (we published the main idea in 2005) but it remains controversial and we hope the talk will generate some discussion of the ideas involved.

This talk is part of the Isaac Newton Institute Seminar Series series.

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