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Turbulent transport and mixing of a passive scalar blob in a confined vessel are studied. The mixing process is due to the fluid dynamics generated by a single rod with a figure-eight shaped motion. A volume penalization method in a classical Fourier pseudo- spectral code is used to define the confined vessel and to impose the dynamical motion of the rod. The two-dimensional incompressible Navier-Stokes and advection-diffusion equations are solved and its dynamics are compared to advection-diffusion by Stokes flow. The decay of scalar variance in Stokes regimes, for different Schmidt numbers, is compared with the one obtained in Ref. [1] for chaotic mixing. Afterwards, the influence of Reynolds and Schmidt numbers onto turbulent mixing is investigated. The existence of power- laws for time evolution of the scalar variance is particularly underlined. In turbulent regimes, the mixing is found to become more efficient for increasing Reynolds and Schmidt numbers. The product of these two numbers, the large scale Péclet number, does not seem the only parameter which controls the mixing rate.
Author(s):
Benjamin Kadoch
Aix-Marseille Université / IUSTI
France
Wouter Bos
Ecole Centrale de Lyon/ LMFA
France
Kai Schneider
Aix-Marseille Université / M2P2
France