Events in MathSys and Complexity Science
This is a calendar page detailing events within the MathSys CDT. It also acts as a booking diary for the Seminar Room D1.07. To book D1.07 please email Sheetal.Sharma@warwick.ac.uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
MathSys CDT events have priority for D1.07 room bookings.
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Complexity Forum
Location: Maths B3.02
Professor Bernhard Mehlig
(Department of Physics, Gothenburg University, Sweden)
Unmixing in random flows
We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyse this 'unmixing' effect by calculating the Lyapunov exponents for dense particles suspended in such a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time of the random flow (that is, the regime of large Stokes number). In this limit Lyapunov exponents are obtained as a power series in a parameter which is a dimensionless measure of the inertia. We report results for the first seven orders. The perturbation series is divergent, but we obtain accurate results from a Pade-Borel summation. We deduce that particles can cluster onto a fractal set and show that its dimension is in satisfactory agreement with previously reported in simulations of turbulent Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow.
Unmixing in random flows
We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyse this 'unmixing' effect by calculating the Lyapunov exponents for dense particles suspended in such a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time of the random flow (that is, the regime of large Stokes number). In this limit Lyapunov exponents are obtained as a power series in a parameter which is a dimensionless measure of the inertia. We report results for the first seven orders. The perturbation series is divergent, but we obtain accurate results from a Pade-Borel summation. We deduce that particles can cluster onto a fractal set and show that its dimension is in satisfactory agreement with previously reported in simulations of turbulent Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow.