  Active matter embraces systems that self-organize at different length and
time scales, often exhibiting turbulent flows. Here, we use a
quasi-two-dimensional nematically ordered layer of a protein-based active gel
to experimentally demonstrate that the geometry of active flows, which we have
characterized by means of the statistical distribution of eddy sizes, can be
reversibly modified. To this purpose, the active material is prepared in
contact with a thermotropic liquid crystal, whose lamellar smectic-A phase
tiles the water/oil interface with a lattice of anisotropic domains that
feature circular easy-flow directions. The active flow, which arises from the
motion of parabolic folds within the filamentous active material, becomes
effectively confined into circulating eddies that are in registry with the
underlying smectic-A domains. Based on topological arguments applied to the
circular confinement, together with well-known properties of the active
material, we show that the structure of the active flow is determined by a
single intrinsic length scale. The role of this length scale thus reemerges
from setting the decay length in the exponential eddy size distribution of the
free turbulent regime, to determining the minimum size of circulating eddies
featuring a scale-free power law. Our results demonstrate that soft-confinement
provides with an invaluable tool to probe the intrinsic length and time scales
of active materials, and pave the way for further exploration looking for
similarities and differences between active and passive two-dimensional
turbulence.
