Three-dimensional flow structure in a kinesin-driven active gel*

An active gel of kinesin-driven microtubule bundles gives rise to a turbulent-like flow which, for a specific set of toroidal geometries, spontaneously gives rise to a coherent azimuthal flow (Wu \textit{et al.} \textit{Science} (2017)). Here we present results from a two-color velocimetry that simultaneously measures (i) the planar components of velocity of the active microtubule bundles in several $r-\theta$ planes at multiple $z$ stacks and (ii) the three-dimensional motion of passive tracer particles throughout the entire system. This technique is used to reconstruct the structure of the active flow for both coherent and non-coherent (``turbulent'') systems. We present data on the activity of the gel as a function of confinement as well as the mean velocity and fluctuating profiles for the cases in which a coherent flow develops. In addition to the azimuthal flow around the torus, we observe large-scale vortex-like secondary flow structures that form and break up in the $r-z$ plane.