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

Authors:
Preprint
Publisher website
Google Scholar
Abstract
Coherent structures in two-dimensional Navier-Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. In spite of the steadily growing amount of literature with regard to flow coherence, the general influence of spatiotemporal coherence on the structure formation process that is associated with the inverse cascade of kinetic energy, is still subject of current research. 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 to determine the respective thresholds required by these methods based on physical properties of the flow. The resulting comparability allows to identify characteristic differences between the employed structure detection techniques. We observe that all schemes exhibit qualitatively similar results with respect to the cascade behavior. Furthermore, coherent structures contribute less to the inverse energy cascade than the residual incoherent parts of the flow. This can be understood by an increased misalignment of strain-rate and subgrid stress tensors within coherent structures. At the same time, these 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 by means of vortex thinning, which is analysed in terms of a recently introduced multi-scale gradient approach [G. L. Eyink, J. Fluid Mech., 549:191-214, 2006].

This publication has 46 references indexed in Scilit: