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C7 (N): Dense active suspensions in the chaotic regime

The goal of the project is to investigate active particle motion in a soluble medium (bacteria or active colloids) in the chaotic flow regime (“turbulence”) on an essentially two-dimensional manifold. We employ three differ-ent methods bridging the scales from microscopic particle motion to the continuum. On the smallest scale, we conduct (i) direct numerical simulations. This will be the basis for the construction of a (ii) mixture model founded on the Eulerian spatial averaging leading to an effective flow model. Built on this, a (iii) probability density function description and, in turn, its group theoretical properties will be the final goal to understand the complete and detailed statistics of the problem.

Funding for this project has started in July 2018.


Statistical theory of helical turbulence
B. Deußen, D. Dierkes, and M. Oberlack
Physics of Fluids 32 (6), 065109 (2020);
doi:10.1063/5.0010874

A statistical theory for homogeneous helical turbulence is developed under the condition of strong symmetry. The latter describes reflectional symmetry in planes through and normal to the helical unit vector eξ, which can be achieved by demanding that the mean velocity is zero. The two-point velocity correlation, the pressure–velocity correlation, and the two-point triple correlation are expressed by scalar functions in the helical unit vector system. By introducing the continuity equation for the correlations, the number of unknown functions can be reduced to such an extent that ultimately, a single scalar transport equation remains. Furthermore, a two-point Poisson equation is derived to express the pressure–velocity correlation in terms of the triple correlation. From the two-point version of the transport equation, the single-point limit is derived. Using the single-point equation, it can be shown that all velocity components are generally non-zero. Therefore, it is concluded that the phenomenon of vortex stretching is present in the helical coordinate system. Finally, the theory of axisymmetric turbulence is derived as a limiting case of helical turbulence to show consistency with former work.

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