Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow

TL;DR

This paper explores how viscoelastic fluids in a two-dimensional Kolmogorov flow transition from steady to complex, turbulent-like states as elasticity increases, revealing elastic turbulence phenomena.

Contribution

It demonstrates the transition to elastic turbulence in a 2D viscoelastic flow using direct numerical simulations, highlighting the role of elastic forces and propagating patterns.

Findings

Flow transitions from stationary to fluctuating states at critical Weissenberg numbers.

Flow exhibits complex, mixing-enhanced behavior with elastic turbulence features.

Propagating filamental patterns emerge even with minimal inertial effects.

Abstract

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial non-linearities, thanks to the feedback of elastic forces on the flow.