Coherent structure detection and the inverse cascade mechanism in two-dimensional Navier-Stokes turbulence

TL;DR

This study compares various methods for detecting coherent structures in 2D turbulence, analyzing their sensitivity and role in the inverse energy cascade, revealing that structures influence large-scale flow but contribute less to energy transfer.

Contribution

It introduces a comparative analysis of structure detection techniques based on a vortex scaling phenomenology, enhancing understanding of their sensitivity and role in turbulence dynamics.

Findings

Coherent structures contribute less to energy flux than incoherent parts.

Detected structures significantly deform the energy spectrum at large scales.

Structures exhibit stabilization through nonlinear cross-scale interactions.

Abstract

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.