  Coherent structures in two-dimensional Navier-Stokes turbulence are
ubiquitously observed in nature, experiments and numerical simulations. The
present study conducts a comparison between several structure detection schemes
based on the Okubo-Weiss criterion, the vorticity magnitude, and Lagrangian
coherent structures (LCSs), focusing on the inverse cascade in two-dimensional
hydrodynamic turbulence. A recently introduced vortex scaling phenomenology [B.
H. Burgess, R. K. Scott, J. Fluid Mech., 811:742--756, 2017] allows the
quantification of the respective thresholds required by these methods based on
physical properties of the flow. The resulting improved comparability allows to
identify characteristic relative differences in the detection sensitivity
between the employed structure detection techniques. With respect to the
inverse cascade of energy, coherent structures contribute, as expected,
substantially less to the cross-scale flux than the residual incoherent parts
of the flow although the energetically dominant coherent structures lead to an
important large-scale deformation of the energy spectrum. This cascade
inactivity can be understood by an increased misalignment of strain-rate and
subgrid stress tensors within coherent structures. At the same time, the
structures exhibit strong and localised nonlinear cross-scale interactions that
appear to stabilize them. We quantify and interpret the resulting shape
preservation of coherent structures in terms of a multi-scale gradient approach
[G. L. Eyink, J. Fluid Mech., 549:191--214, 2006] as the depletion of strain
rotation and vorticity gradient stretching while the dynamics of the residual
fluctuations are consistent with the vortex thinning picture.
